This is a sentence in lines 153-154 of chapter XVIII of Lingua latina per se illustrata. Familia Romana:
Cum pater tuus abest, oportet tē epistulās ad eum scribere.
Is there any reason why ad eum (preposition ad followed by the accusative singular pronoun eum) is used to express the indirect object of scribere? Could I also write it this way, using the dative personal pronoun sibi?
Cum pater tuus abest, oportet tē epistulās sibi scribere.
I agree with cmw that it is useful to compare the predicative frame of scribere with that of mittere. Let's start with the "easier" case, i.e. the one of the verb mittere. In his Oxford Latin Syntax (vol. 1), Pinkster (2015: 142) says the following:
The notions of ‘bringing’ may imply the shift of ownership of a certain entity, but they may also imply the transportation from one owner or place to the other. The verb mitto ‘to send’, for example, may denote both transportation of an entity from one location to another and transfer of an entity from one person to another. In the first case, it has a direction third argument, in the second, a recipient third argument. Examples are (k) and (l), respectively.
(k) Recita quas ad Neronem litteras misit. (‘Read the letter which he sent to Nero.’ Cic. Ver. 1.83)
(l) . . . in litteris quas Neroni mittis, . . . (‘ . . . in the letter you send Nero . . . ’ Cic. Ver. 1.80)
In his paper [NB: written in Spanish] devoted to the interesting alternation Litteras {Neroni/ad Neronem} mittere, Baños (1996) concludes that in Classical Latin the use of the dative case with the verb mittere can be typically associated to a beneficiary reading, whereas the spatial/directional relation is expressed by the PP (Prepositional Phrase) ad + accusative (NB: Baños's conclusion is very solid for Caesar and is also claimed to hold for Cicero). So note that his conclusion is not exactly the same as that of Pinkster (2015: 142), who posits the following meaning-form/case associations with the predicative frame of mittere: "shift of ownership" is associated to the dative case, whereas the spatial "transportation from one owner or place to the other" is associated to the PP ad + accusative.
As noted, a similar alternation is found with the verb at issue here: scribere, on which Pinkster (2015: 143) says the following:
A number of communication verbs also have two alternative expressions: either with a direction argument or with an addressee argument. Instances include the verbs nuntio ‘to report’ and scribo ‘to write’ in the examples (m)–(p). The direction expression is relatively more frequent in Cicero’s letters (which were indeed sent and were not meant for publication) than in the letters of Seneca and Pliny.
(m) Nunc tu illum si illo es missurus, dice, [de]monstra praecipe / quae ad patrem vis nuntiari. (‘Now if you’re going to send him there, tell him, show him, teach him what you want to be reported to your father.’ Pl. Capt. 359–60)
(n) Aperite, aperite, heus, Simoni me adesse aliquis nuntiate. (‘Open up, open up! Hey, someone announce to Simo that I’m here!’ Pl. Ps. 1284)
(o) . . . quem ad modum tute ad Neronem scripsisti . . . (‘ . . . as you wrote to Nero yourself . . . ’ Cic. Ver. 1.84)
(p) Scripsi tibi quae hic gererentur. (‘I am writing to tell you what is going on here.’ D. Brut. Fam. 11.11.1)
Furthermore, it is worth pointing out that there are some examples where the verb mittere coappears with the communication verb at issue here: scribere: cf. the (spatial) direction argument ad te with the (non-spatial) addressee argument mihi.
Quo die ego ad te haec misi, de Pilia et Attica mihi quoque eadem quae scribis et scribuntur et nuntiantur. (Cic. Att. 12.40.5);
More interestingly, in the following example from Cicero the same verb scribere selects the directional argument ad te in the relative clause but the (semantically speaking, non-spatial) addressee argument mihi in the main clause.
Quod ad te scripseram ut cum Camillo communicares, de eo Camillus mihi scripsit [te] secum locutum. (Cic. Att. 11.23.1);
So, coming back to your example from Lingua latina per se illustrata (Cum pater tuus abest, oportet te epistulas ad eum scribere), it seems plausible to conclude that the use of the prepositional phrase ad eum is more natural (and frequent! see cmw's answer) in this directional context, which involves a Figure object epistulas ('Figure' = the moving entity) and a Ground (ad) eum ('Ground' = the entity which acts as a spatial reference point for the motion of the Figure). See page 1 of this link for the so-called "Figure-Ground organization". This said, it should also be noted that the existence of examples without an explicit Figure object (e.g. see Cicero's ex. above: tute ad Neronem scripsisti) is not incompatible with this explanation: conceptually speaking, the scriptum object incorporated into the verb is the Figure object that goes to Nero, i.e. the Ground (in this case, the final destination of the path).
Finally, what about an example with a dative pronoun like oportet te epistulas ei scribere? As noted, in the very particular construction of epistulas scribere (see cmw's pertinent remark below on the conventionality of the collocation dare litteras), there is a strong preference for using the directional PP ad + acc., whereby in this very specific context (epistulas scribere) the use of the dative ei is not excluded but is marked and less frequent in some classical authors (e.g. in Cicero; see cmw's pertinent remark in his answer. See also Pinkster's short remark above on some relevant usage differences between Cicero and later authors like Seneca or Pliny).
EDIT
In the comment section below cmw and I commented on an interesting example that shows that a directional PP (ad te) and a dative (Philogono, liberto tuo) can even coappear, which shows that these two constituents do not have the same function (note also that they could not be coordinated either).
sed tamen, quoquo modo potui, scripsi et dedi litteras ad te Philogono, liberto tuo, quas credo tibi postea redditas esse (Cic. Q.fr. 1.3.4)
In agreement with what I have said above, it seems clear that with these verbs the PP formed by the preposition ad plus a noun in the accusative case is used to express "the final destination of the path". It is clear that Cicero's brother is the (final) owner of the letter but what is semantically construed through the PP ad te is not the beneficiary nor the non-spatial receiver (which are meanings expressed by the dative) but the final destination of a path. As for the dative Philogono, liberto tuo, it expresses the (immediate) receiver of the letter but not the final one, which, as noted, is expressed by the spatial expression ad te. So when a dative is used, it is a non-spatial receiver, i.e. unlike the PP formed by ad plus acc., the dative does not grammatically express a spatial path.
Here are two translations of this example (NB: from time to time it is useful to recall that one should not analyze the Latin syntax of examples on the basis of their translations. Translations can be helpful to understand how the Latin examples are to be interpreted but are not necessarily useful as for how they are to be analyzed. For example, Baños (1996) raises this important point when noting that the alternation Litteras {Neroni/ad Neronem} mittere is not found in Spanish, whereby the translations of the dative and the ad+acc. constituent are often the same in this Romance language).
'Nevertheless, to the best of my ability, I did write a letter to you, and gave it to your freedman Philogonus, which, I believe, was delivered to you later on.' (Evelyn S. Shuckburgh, 1908; Perseus).
'However, I did write to you as best as I could and gave the letter to your freedman Philogonus. I expect it was delivered to you later.' (D. R. Shackleton Bailey, 1972/2002; Loeb)
This information is easily found in Lewis and Short, a comprehensive dictionary of Latin.
Under scribo (see the parts in bold):
So freq. of written communications, letters; usually with ad aliquem (less freq. alicui) or de aliquā re: “nihil habeo, quod ad te scribam, scribo tamen, non ut te delectem, etc.,” id. ib. 14, 12, 3: “senatusconsultum si erit factum, scribes ad me,” id. ib. 5, 4, 2; cf.: “scripsi etiam ad Camillum, ad Lamiam,” id. ib. 5, 8, 3: “in quā (epistulā) de agro Campano scribis,” id. ib. 2, 16, 11: “ut nuper me scis scripsisse ad te de Varronis erga me officio, etc.,” id. ib. 2, 25, 1; cf.: “Hermae tui Pentelici, de quibus ad me scripsisti,” id. ib. 1, 8, 2; 1, 9, 2 et saep.— With ut, ne, etc.: “velim domum ad te scribas, ut mihi tui libri pateant,” Cic. Att. 4, 14, 1: “ad me scriberet, ut in Italiam quam primum venirem,” id. ib. 11, 7, 2; 5, 11, 6.— With dat.: “consules Fulvio, ut ex Falisco, Postumio, ut ex Vaticano exercitum ad Clusium admoveant, scribunt,” Liv. 10, 27; 42, 27; Tac. A. 1, 29.—With ne: “Scipioni scribendum, ne bellum remitteret,” Liv. 30, 23.—With simple subj.: “scribit Labieno, si rei publicae commodo facere posset, cum legione ad fines Nerviorum veniat,” Caes. B. G. 5, 46 fin.—In Tac. also, with inf.: “scribitur tetrarchis ac regibus, jussis Corbulonis obsequi,” Tac. A. 15, 25 fin.
It's possible to use the dative here (which would be ei, not sibi, because the subject isn't writing letters to himself), but in reading Cicero's letters (a good example of actual everyday Latin not written for publication) ad + te is the common way to express writing someone a letter, with the implication that you're sending them a written message.
Some other words use ad + acc. where in English you might expect the indirect object, such as mitto and do, especially when they're paired with litteras (cf. ille litteras ad te mittat, Cic. Phil. 7.5). In that case, it might be helpful to think about it in terms of the physical action: the object is sent and moves spatially towards a person. Similarly, when you write something, you're crafting a letter that is being spatially sent to that person. Thus ad is used.
