My cousin is 15 years old and married. She recently came to Germany with her husband (25 years old). The marriage is not accepted here. Why not?

Your cousin married abroad.
In Germany, marriage is only permitted after your 18th birthday.
When both parties are 18 years old.
Sometimes a marriage is permitted when one of the partners is only 16 or 17 years old.
This is decided by the family court.
An application must be made before the marriage.

If somebody is younger than 16 years old they may not be married in Germany.
Therefore, a marriage concluded abroad is not recognised here.
The reason for this is that people must be mature enough for a marriage.

In Germany the state must protect children and young people.
The state must be sure that young people marry voluntarily.
This means: nobody forces or convinces somebody to marry (for example, the family).
They must have decided for themselves.
This is the reason why the marriage age is determined in this way.