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As you can see below, he disagrees because "a marriage sealed by fate is stronger than any oath." As you can see the marriage or contract between two people is considered stronger than the bonds of blood. Oaths are taken through "free will," (well, we always hope they are), whereas ties of blood involve no choice at all.
What's that? Proclaim your fine authority.
We chase out of their homes those criminals 
who slaughter their own mothers.
What about a wife who kills her husband?
That's not blood murder in the family.
What about Zeus and his queen Hera—
your actions bring disgrace on them.
You ignore the strongest bonds between them.
Your claim dishonours Aphrodite, too,
goddess of love, from whom all men derive 260
their greatest joys. With man and woman
a marriage sealed by fate is stronger
than any oath, and justice guards it.
Now, if one partner kills the other one,
and you're not interested in punishment, 
if you feel no urge to act, then I say
the way you chase Orestes is unjust.
I don't see why in one case you're so harsh
when you don't really care about the other.
However, goddess Athena will take charge— 270
she'll organize a trial.