If a Mexican went around calling himself Spanish would he be lying?

Ok so i'm not Spaniard and i'm not from Spain, i'm Mexican. My great grandparents from about one hundred generations ago came from Spain. The Spaniards colonized Mexico and most of Latin America. In many cases European blood lines have stayed the same. I wrote on a census that I'm Spanish, a friend of mine said "Why did you write that you are Spanish? You are not Spanish you are Mexican." My response was Mexicans are Spanish, why do you think Mexicans speak Spanish? I am not Aztec or Maya. I am fool blooded Spanish even tho I identify with Mexico not Spain. If I went around telling people i am Spanish would i be lying?