Why "Abolition damaged rival states" is easier to support

Because it is an effect claim rather than a motive claim.

Effect claim:

Abolition weakened the slave-based economy of the Confederacy.

Motive claim:

Lincoln abolished slavery primarily because he wanted to weaken the Confederacy.

The first requires evidence about what happened.

The second requires evidence about what Lincoln intended.

Intentions are usually harder to prove than consequences.