I think there was a lot more context to it that you missed off too though. The points on their own were an issue obviously, but we'd also lost a few games in Europe on top of the league ones, the City draw was in a game where they went down to 10 in the first half, the defeats you're talking about included two 3-0s, a 4-0, and a 5-2 (at home), and we had played about 15 games in all competitions without ever looking like a coherent team. It wasn't like we were just coming off slightly worse in tight games, we looked absolutely rancid.
Koeman wasn't a good manager for us, he was never going to be here long term and was only hired because Moshiri wanted a big name, he was phoning it in from the golf course right from the off and sacking him was the right thing to do. Silva is a totally different argument because the whole point of getting someone like him was supposed to be to have a style of play, a progressive young manager who was going to be here for a while and put their own stamp on the club, but then we ripped it all up as soon as we hit a bump in the road and lurched back in another direction again, there's much more reason to think that we should have stuck with Silva for the long term benefit.
EDIT - Sorry I genuinely assumed this was the new manager thread so i'll shut up now as it's off topic.