Ujm is correct that those who forbade it (especially rav avigdor miller) were American and able to read English historical accounts. The machlokes is more about the facts than halacha. Everyone agrees that if something has AZ roots it would be assur even if now it is not viewed that way (think of Halloween). Actually, the maharik in siman 98 says that this is the precise reason that a non jewish custom without a clear meaning is not allowed, because we’re worried that there’s a forgotten AZ component, and if so, it would be assur even if now it is merely cultural etc.
Mother’s day is a completely cultural holiday, as is the 4th of july and other secular national days. It is of note, however, that father’s day is not observed by most frum people, but mother’s day is…hamyvin yovin.
The oft quoted refrain of “we give thanks every day” does not speak to the issues involved with Thanksgiving, from a halachik save hashkofic perspective. We acknowledge that there are opportune times that we focus on a given theme, lehavdil. Aside from the halachik issues above, there is a deeper hashkofic problem as well. Jewish holidays, as explained by the ramchal, have a “koach hazman”, a spiritual power inherent in the day itself. The powers of geulah were the reason why the yidden left on the 15th of Nissan; pesach isn’t merely a commemoration of what happened in the past, but rather a time when the avodah associated with geulah, from one’s personal shi’bud, comes to the fore. Chanuka we celebrate torah she baal peh. But this is the reason why leshana acheres kavuah, the chachamim only instituted chanukah the following year. Says the ohr gedalyahu, it was because the chachamim wanted to see if the spiritual powers they felt on chanuka returned the next year; if they did, it was worthy of being a yom tov.
Acknowledging secular holidays (aside from showing patriotism to our host country on, say, 4th of july, veterans day, memorial day, etc) dampens our understanding of koach hazman and makes us establish holidays that have no bearing on us. There’s nothing special about this day that has a shaychus with hakaras hatov; that is something we focus on during pesach, chanukah, sukkos, purim, and other times whej gratitude is one of the central themes.