You find the real “meaning” of language by looking at how it’s used in actually used, not by analyzing individual words in an overly literal way or, what I see all the time as a college instructor, simply pointing to what’s written in the dictionary, because even dictionary definitions evolve over time to reflect changes in popular usage.
“Hobby jogger” as a term doesn’t really have much to do with “hobby” in the sense in which it’s normally used, which has a benign or positive connotation. “Hobby jogger” is a pejorative used in a community to express distant for others engaging in the same activity, but at a level of dedication that the people using the term consider inadequate, a level of talent they consider mediocre at best, and/or for motivations they consider to dilettantish.
Other communities have similar terms. For chess players, it’s “patzer.” A long time ago, poets and other literary types used the term “poetaster,” although that’s not really much in usage anymore.
The term conveys a sense of smug superiority, although the people using it would probably insist that what they’re actually doing is serving a useful role as gatekeepers for the forums, guarding the integrity of the sport, encouraging higher levels of dedication, and so forth. The term also serves to reinforce a sort of group identity, with the person using it announcing his/her membership in the group and creating in an atmosphere in which others feel pressure either to agree or keep quiet.
If we’re going to talk about specific times, I think there are in fact two categories: 1) times not to be embarrassed by and 2) times to be proud of. For 1), if someone on here had a sub-17:00 5K personal best, then that person probably wouldn’t be called a “hobby jogger” unless he (I’m using a man for these examples) were bragging about it, in which case it would be pointed out that he wasn’t anywhere even close to semi-elite status. For 2), if someone had a sub-14:00 5K (or maybe a marginally better time), he would be respected and others would ask for and mostly defer to his advice on matters of training. The person in 1) would be called out as a “hobby jogger” as a way of putting him in his place. The person in 2) would be considered definitely not a “hobby jogger,” although if he were being excessively arrogant, I’m sure people would still find some way to call him out.
Frankly, I “hobby jogger” off-putting, and I seriously doubt the people regularly using it are, have been, or will ever be true national-class athletes. However, many others have made this point, and yet the term has been used here often enough that unfortunately I think it will probably stick around for a while longer. I’d like to be proven wrong, because if people here are serious about being ambassadors of the sport, then they’ll realize that coming across as an arrogant, exclusionary in-group is counterproductive.