The last line is most telling -- it's backwards! Securus doesn't mean making something else safe, but rather it is the outcome of being made safe. Likewise, if something is securus, it's not that others didn't place care on it, but it itself lacks care.
If king is protected by a guard, the king is securus -- he no longer has to care about his well-being. ...
Though Gaffiot claims the adjective eugenēus is borrowed from Greek εὐγένειος, I find that hard to accept on semantic grounds: εὐγένειος means 'well-bearded' (in the case of men) or 'well-maned' (in the case of lions), not 'well-bred'. I (and Lewis & Short with me) think it much more likely it was instead derived from εὐγενής, which means the same thing ...
Reduction of the problem
It is good to preprocess the data and reduce the words into simpler constituents within Latin.
We can reason as follows:
parens < parere
parturitio < parturire < parere
partitio < partire < pars
This reveals that parens and parturitio are already well linked within Latin, both coming from parere.
Now it remains ...