I wouldn't describe it as a "lie" so much as challenging the socially prescribed link between sex and gender. Trans people know they're biologically male, and they know you probably know it. But they're challenging the social expectations that get associated with that.

The same analogy can again be drawn with homosexuality. 100 years ago, many people believed that it was a biological fact that men preferred women and vice versa. To hear a man proclaiming that he prefers men, or a women proclaiming she prefers women, sounded to them like a lie. But as society progresses, social norms tend to relax. In fact there are people to this day who cannot quite accept the idea that homosexuals might genuinely exist. To such people, seeing a gay couple kissing feels like being expected to ignore a biological fact.