Not just Christmas! The date of Easter was designed to coincide with pagan celebrations of spring (and its name is actually taken from a pagan goddess). St. Valentine's Day was the result of an effort to replace a Roman celebration with one that appealed less to prurient interests.
Actually, a great deal of the Christian religious calendar is related to older pagan festivals. That's not unreasonable; many of those festivals had a character particularly suited to a particular time of year, and Christians found it useful to schedule their celebrations in a similar pattern because
(a) they have themes equally suited to those periods in the northern hemispheric seasonal cycle; and
(b) that way, Christians celebrations would coincide somewhat with the pagan equivalents, which made for less friction.
In some cases, simply practical considerations arose. The restricted diet of Lent was particularly apt to the period in spring when the winter stores are running low and very few crops have been growing long enough to be productive.
Some Christians make a big deal about the pagan associations. For example, the eve of All Saints (or All Hallows' Eve, or Halloween) is widely known for its pagan associations and not observed by many Christians. Similarly, the Puritan regime in England suppressed Christmas celebrations; Dickens' "A Christmas Carol" was connected to efforts to revive them, a considerable time later.
But there's no particular reason to emphasize the pagan roots in Christian teaching, so many Christians don't know some of the sources. In that sense, we ignore it, but we don't see any reason to consider it a big deal.
And in some cases we translate traditional symbols to new meanings. I grew up hearing my father preach, many times at Christmas, a sermon interpreting the Christmas tree (often erected in the sanctuary of the church) in terms of Christian symbology, and my awareness of the pagan roots of the tree tradition in no way renders his Christian interpretation invalid.