Why do we discourage converts? I know that Naomi did so with Rus, but Moshe doesn't seem to do so with Yisro. Why wouldn't Judaism want to encourage converts? Furthermore is it a responsibility merely of the Rabbi performing the conversion or of any Jew who meets the convert (if it is the former how do we understand why Naomi dissuaded Rus)?
The way a local Orthodox rabbi explained it to me is this:
Being Jewish is harder than being a gentile, and (for gentiles) it's totally optional. Gentiles do not need to become Jews to merit a good life and olam haba.
However, once someone does become a Jew he has greater obligations. Doing (or not doing) certain things now is a sin where it was ok before. The sinning Jew is thus in a worse place in his relationship with God than he would have been had he not converted. Conversion is also permanent; you can't decide to "go back" and thus stop sinning.
Further, being a Jew isn't always easy in the world. We're persecuted, and throwing your lot in with us signs you up for that.
So partly out of a desire to protect and partly to not increase sin, we push back to make sure the candidate knows what he's getting into and is sincere. The Rambam (Issurei Biah Chapter 14, h/t DoubleAA) says we point out some of the easier and harder mitzvot that will now become obligatory, and we inform him of punishments and rewards. If the candidate persists, we welcome him in.
This Chabad answer to a question from a prospective convert addresses some of these topics well.
Because discouragement isn't supposed to be forever -- we stop after three times (based on Naomi's three attempts to dissuade Rut, according to Rut Rabbah 1:16) -- I would think that it's inappropriate for people other than the rabbis approached by the prospective ger to do this discouragement. It's their job, they'll do it, and if you also do it you're adding to the obstructions. As for why Naomi did it anyway, two thoughts: (1) the formal process may not have been so codified then, and (2) that's an awful long journey to make just to be rejected at the end. I don't think we should take Naomi as a model for how "regular Jews" should treat would-be converts today; instead our tradition takes it as a model for how a beit din or rabbis behave.