When you are disparaging, you express negative, low opinions in order to lower someone's reputation. Your friend will probably not appreciate it if you make disparaging comments about his girlfriend.
In its original use, disparage meant "to marry unequally," and it was considered a disgrace if a very wealthy son married, say, the kitchen maid. Nowadays we use disparaging for any derogatory or belittling expression or comment. If just won an Olympic gold medal, it's just rude and unnecessary to be disparaging about the silver medalist in an interview. Making disparaging remarks about your wife's cooking is unlikely to result in better food. She'll just get mad.
