Was Martial the school ground bully or is there an underlying meaning?

I believe that in Martial's epigrams, epigrams VII.3, XXII.46, II.38 are satire, while epigram I.32 is a parody.

Martial's epigram I.32 can be classified as a parody because it's rude and makes fun of something stupid (being Sabidus in the passage), and has no higher meaning. This epigram doesn't seem to me to even have the slightest bit of higher meaning besides just insulting the person. If Martial gave an explanation for why he doesn't like Sabidus, then there would be some form of higher meaning but he doesn't and rather just cruelly insults Sabidus.

Martial's epigrams VII.3, XXII.46, and II.38 are satire. Although Martial criticizes people in these epigrams, there is a higher meaning in each of them. In epigram II.38 Martial insults Linus, but actually provides a reason for why he's insulting Linus. Martial's reason for going to the farm in Norment could be partly because of Linus which makes this satire. In epigram XXII.46 Martial is actually complimenting this person. In this epigram Martial criticizes specific traits in a person and then amends them by saying they are also the opposite of that. Epigram VII.3 Martial criticizes Pontilianus' works but actually brings up a valid point in society that one person may not send something to another person for fear of receiving a bad item in return.

Martial can be mean but often brings up valid points and flaws in society that are "stupid."