The whole logic of not wishing them Merry Christmas as it would be equivocal to recognizing the Trinity of God, and recognizing that Jesus is the begotten Son of God, is not a good logic. It is a logic which doesn't care what others think, a logic which spreads suspicion among people, and a logic that can possibly breed enmity based on religious differences.
If Christians have the same logic, they won't respect our Ramadan. They won't let us celebrate Maulid Nabi, they won't let us have our Azans in loudspeakers, they would say that Muslims are followers of Antichrist!
There's this whole notion among Christians (of course I am talking about the freaking fundamentalists) that we Muslims are heretical, deviant, and violent followers of an excommunicated church, manipulated by a false Messiah called Muhammad. Us not wishing Merry Christmas to Christians might fuel this thought among the Christians, increasing their enmity toward us, and consequentially this will increase our enmity towards them.
There is no communication where there is enmity.