Don't transgender individuals reinforce traditional gender roles?

Genuine question, don't hate.

Transgender individuals often argue that gender is a social construct, which I agree with to some extent. As a society, we have indeed assigned certain traits, behaviors, and roles as "feminine" or "masculine." However, these traits should not inherently dictate a person's actions, interests, or identity based on their biological sex. For example, being born a woman does not mean one must like cooking or engage in activities deemed "feminine." Similarly, having interests traditionally labeled as "masculine," such as sports, should not diminish one's identity as a woman.

This leads to the question: What does it truly mean to "be" a woman or a man? Beyond biological sex, there is no clear, objective set of rules governing one's identity as male or female. People who identify as transgender often express feelings such as "I feel like a man rather than a woman." But what does this mean? If it is merely an affinity for things culturally associated with masculinity, wouldn't that simply align with the concept of being a "tomboy" rather than necessitating a change in gender identity?

What does it actually mean to "feel" like a man or a woman? Arent these statements inadvertently reinforcing traditional gender roles by suggesting that certain interests, behaviors, or ways of feeling are inherently tied to one's gender?