Why do some people think that just because you are gay that means you are transgender?

The other day I was speaking to my parent about seeing the Danish Girl, and they said not to because that will make you think about living a transgender life style. Now I admit, years ago I thought about being transgender a couple of times, but it is a lifestyle that I definently do not feel like inside as a feel truly like a gay man. I said to my parent that that isn't true because I am gay and feel like my biological gender is male. This made me slightly again question being transgender,but then I came to the same place where I thought there is no way I am transgender, I am 100% gay and male. Why do some people think this though?