How do you answer the charge that apologetics is divisive?
By acknowledging that in certain ways it is, in certain ways it isn't, but that in any case we must keep in mind that divisiveness isn't necessarily a bad thing.
Look at the ministry of Jesus. It was he who said,
Do you think that I have come to establish peace on Earth? No, I tell you, but rather division. From now on a household of five will be divided, three against two and two against three; a father will be divided against his son and a son against his father, a mother against her daughter and a daughter against her mother, a mother-in-law against her daughter-in-law and a daughter-in-law against her mother-in-law (Lk 12:51-53).
Christ also taught the need for people to heed his appointed messengers in the Church when he said, "Whoever listens to you listens to me. Whoever rejects you rejects me. And whoever rejects me rejects the one who sent me" (Lk 10:16).
Paul stressed the importance of being faithful to Christ by adhering to his teaching as it has been passed down by the Church. To Timothy he wrote, "Take as your norm the sound words that you heard from me, in the faith and love that are in Christ Jesus. Guard this rich trust with the help of the Holy Spirit that dwells within us" (2 Tm 1:13).
Although Paul told Timothy to avoid foolish quarrels, he still instructed him to correct opponents with kindness, not just ignore their errors. To Titus Paul wrote, "Avoid foolish arguments, genealogies, rivalries, and quarrels about the law, for they are useless and futile. After a first and second warning, break off contact with a heretic, realizing that such a person is perverted and sinful and stands self-condemned" (Ti 3:9-11).
These passages indicate the importance of proper belief without minimizing the need for charity. Truth divides, although it need not involve acrimony.
Apologetics is the business of contending for the faith (Jude 3), without necessarily being contentious. In fact, when properly applied, apologetics can bring us closer to non-Catholics (and non-Christians) through better understanding of one another's beliefs.