Maybe?

What was the photo?

It's one of their goals, yes

no fault divorce ruined the private investigator industry

There's no "maybe" about it. It's documented. Listen to the extremely American podcast

Of course that is exactly their goal. It's not like they're trying to hide it.

In short, this is some BS tweet (and blatant propaganda) that seemingly has no actual science backing it.

Firstly, no source was provided to back up his claim about female suicide rates. The Statista link from this comment suggests that he is talking out of his ass.

Secondly, that alone would not have been enough to establish a causative relation (no fault divorce => less female suicides). Because correlation does not equal causation.