This question is discussed in John Chadwick's The Decipherment of Linear B; I'll summarize what seem to be the most important factors.
First, the reason that the Cypriot syllabary was deciphered so early was that, by good fortune, there existed both bilingual inscriptions (in Greek/Cypriot and Phoenician) and biscriptal ones (in Cypriot and alphabetic Greek). Such inscriptions are a holy grail for decipherers -- cf. the Rosetta Stone -- but there are none for Linear B.
Second, the similarity between the two scripts isn't actually that great. Chadwick lists only seven signs which are closely similar (including the to in the ἄνθρωπος words you cite), but goes on to say that "about three-quarters of the signs could only be equated by pure guesswork, and we now know that most of the guesses were wrong". Comparison with the Cypriot syllabary was indeed one of the main approaches to try to decipher Linear B, but it didn't go very far.
Third, the graphic principles of the two scripts happen to be different in an importantly misleading way, which the two spellings of ἄνθρωπος illustrate. Namely, syllabic scripts with signs representing CV sequences have trouble writing a consonant that isn't followed by a vowel, like the final -s of ἄνθρωπος. In the Cypriot syllabary, the solution to this problem is to add a dummy vowel, as in this case -se. In Linear B, the "solution" is simply to ignore final consonants altogether and leave them out of the spelling. Now, this is where the partial similarity of the two syllabaries was actually unfavorable to decipherment. This is because this particular sign se happens to be one of the seven that are identical or very similar in both scripts. Now, if Linear B is Greek, and if it operates by the same principles as Cypriot, then since very many Greek words end in -s, one would expect to find very many Linear B words ending in -se, but this is not the case. This seemed like a very strong argument against the idea that Linear B was Greek, since scholars had no way of knowing that the two scripts had different rules for writing final consonants.
Finally, a more abstract but very important factor was the academic-sociological one of scholarly groupthink, so to speak. The dominant idea about the civilization that used Linear B, ever since Arthur Evans discovered the first tablets at Knossos in 1900, was that it was the civilization of the King Minos of Greek mythology, the non-Greek Cretan ruler who according to the legends had once subjugated Athens. Evans wasn't completely wrong, of course, because we now think that the related, yet undeciphered Linear A was indeed the writing of this "Minoan" civilization; he assumed that Linear A and Linear B were variant scripts used to write the same, non-Greek language. (This was all the more natural because until 1939, there were no known Linear B tablets from the Greek mainland, but only from Crete.) Evans' prestige was immense, so much so that Michael Ventris, who would in 1952 prove that Linear B was Greek, wrote in an article in 1940 that "the theory that Minoan [meaning both Linear scripts] could be Greek is based of course upon a deliberate disregard for historical plausibility". Even after Ventris's successful decipherment, it was some years before the last holdouts shook off the idée fixe that the Bronze Age Greeks simply could not have had writing.