There's no contradiction.
A father has the "right" to marry off his minor daughter, as in if he does it, she's married.
Despite that, he's not allowed to do it unless she's old enough to agree and actually agrees.
Similarly, you're not allowed to do various things on Shabbat, but if you do, you've accomplished them. This is obviously true for physical ...
A little complement to the previous answer of @Alex, regarding Kiddushe Kesef.
An interesting Rashi in Yevamot 90b reports that some rabbanim ruled by an interpretation of this Gemara that Kiddushe Kesef is Derabanan.
ואית דאמרי תינח קדיש בכספא דקידושי כסף דרבנן קדיש בביאה דקידושין דמדאורייתא נינהו מאי איכא למימר וטעות גדול הוא בידם דקידושי כסף דאורייתא ...