I can't agree.
I believe the variety of ________ American months is a valuable way to learn all the contributions of people that we, as a country, would otherwise ignore out right completely, or just give the briefest of introductions without any depth or understanding.
As for the most part--
We do have it, a White History Month.
It's called... every month of the year. (We just don't call it that way.)
I'm sorry, but I can't hardly see why White people feel so indignant about one measly month (which is, consequently, the shortest one of the year! Save the leap years...) where we have a concentration on the contribution of Black people.
If ANYTHING... it is a positive embellishment to everyone's knowledge of history.
Did you know that the United States had Italian concentration camps? I didn't even have any idea about that until I joined a celebration of Italian American History Month (October) and found out about it. (Google "Rab Concentration Camp" for the details.) I mean... sure, I learned a lot about WWII but since it's a huge subject... how is it possible to cover every aspect about that? We don't...
And so, we overlook really important details... and if those details so happen to look bad on our part, all the better... right?
June... it's LGBT History month. Now, that's a history that EVERYONE don't know because it's something that's not taught or people actively ignore. How much do you know about the Pink Triangles? Or the overtly gay tones of Ernst Rohm and Hitler? Or the special treatment that the Nazis set aside for gay prisoners (which were, though hard to conceptualize... worse when you compare it to others. Especially at Dachau...)
All these missing bits-- they've eschewed our knowledge of History. That's why we have all these ethnic history months so that we can truly benefit from not only a complete education, but also an education that is compassionate.