Why are stored procedures looked on so negatively?

I've done quite a bit of reading on stored procedures recently and the
consensus seems to be that you shouldn't use them unless you really must.

I don't understand this argument. If you implement all of your logic in
the application then you need to make a network request to the database
server, return the required data from the database to the app server, do
the processing and then return the results. A stored procedure is going
to be a lot faster than that even if you just take away network latency
/ transfer time.

I'm in the middle of building a database and was going to make extensive
use of stored procedures and trigger functions because it makes more
sense for the actions to happen at the database layer rather than in the
app layer.

Should I use them or not?