Richie hates being told to "shut up" it makes him feel bothersome and more annoying that usual thus the birth of the iconic "beep beep". The other losers don't know how shut up makes him feel and he wants to keep it that way, he doesn't want to keep piling his problems up on them.

—imagine Richie hates being told shut up but never voices his strong disliking for the phrase because he doesn't want to build up problems on his friends or the attention put him or the apologies. So he just sits with his bottled up feelings until somebody finally notices his change of moods after being told shut up(probably Beverly) thus the birth of the iconic beep beep—