It does involve hormones as part of the mechanism but puberty is primarily about the maturation of the reproductive system, and how this is experienced depends on one's sex.

To take female puberty as an example, this is the growth and development of the uterus, ovaries, labia and breasts to reach their mature form and function. Most importantly, the menstrual cycle begins, making pregnancy possible.

If a boy has testosterone blocked and is given estrogen instead, he doesn't experience any of this, except perhaps some breast tissue growth and redistribution of fat. His penis and testicles will not develop further and he will probably remain sterile.

However, he doesn't have a female reproductive system, so this is not more similar to female puberty. What he's experiencing is stunted male development, a pharmaceutically-induced eunuch state.

There is no option for him to go through female puberty rather than male puberty, because he lacks the type of reproductive system that would make this possible. As female puberty is not an experience available to him, it makes no sense to describe male puberty as being the "wrong puberty" for him.

Likewise for girls and the impossibility of experiencing male puberty.