[gowld]

Catechist is defined, inside of one line, using terms the audience knows: "Catholic", "lay", and "priest".

The silly objection here is like objecting to the statement "he was a pilot, an airplane driver", because a "driver" drives a car, not a plane.

[throwanem]

That's not a comparable example. There's a lot more to the priesthood than teaching the catechism - Mass and most sacraments, for example, I believe save only viaticum - and "lay priest" is oxymoronic in any case. To someone knowledgeable in the faith, it sounds like the writer is trying to say "deacon", which would still be wrong anyway, and missing nonetheless; to someone lacking such knowledge, it confers an entirely false impression.

As I said, I think OP makes too much of the phrase, but I agree it's entirely risible.