Paul was quoting the LXX as was Matthew:

Gen 2:24  ἕνεκεν τούτου καταλείψει ἄνθρωπος τὸν πατέρα αὐτοῦ καὶ τὴν μητέρα αὐτοῦ καὶ προσκολληθήσεται πρὸς τὴν γυναῖκα αὐτοῦ, καὶ ἔσονται οἱ δύο εἰς σάρκα μίαν. The Septuagint (LXX), edited by Alfred Rahlfs. Published in 1935; public domain.

Westcott and Hort / [NA27 variants] Matthew 19:5 καὶ εἶπεν Ἕνεκα τούτου καταλείψει ἄνθρωπος τὸν πατέρα καὶ τὴν μητέρα καὶ κολληθήσεται τῇ γυναικὶ αὐτοῦ, καὶ ἔσονται οἱ δύο εἰς σάρκα μίαν;

I'm not sure where you got "anti". ?

Since the scriptures do not say "The reason Paul uses anti..." one can only infer, and "infer" is one of my least favorite words. However, possible reasons might be:

• he had a different version of the LXX
• he was translating ad hoc from memory from the Hebrew and this was simply a stylistic preference
• he was highlighting a nuance available in the Hebrew by selecting a different Greek word

I suspect the latter but I'm not versed in Greek literature to appreciate what that might be. If I were pressed to ignorantly guess I would wildly speculate that the anti reading would have a slight sense of a choice being made. That is, some sense of "preferring this, a man will leave...". If this completely indefensible intuition turns out to be on point then it can be linked to the idea that a man does so because it is a good choice (presumably because of the "no one ever hates his own flesh" idea).

For an introduction to the issues around the word "anti" please see this related question:

Hebrews 12:2 "for the joy" or "instead of the joy"?