Evidence of what their actual ages are
I'm not entirely sure where the fandom site did get the information on their dates of birth. I found this IMDB link that says Angelica is the oldest: https://www.imdb.com/title/tt0101188/trivia?item=tr1125424. Again not entirely sure how accurate that is compared to the fandom website. No sources are listed on either site from what I can tell. But this at least indicates it is possible that Angelica is correct that perhaps she is a teen already and Susie and Harold are preteens.
From the standpoint that their ages are correct on the fandom website
I would say it is just in her character to say things like that. Sure she is the same age as Susie and Harold, but she still considers herself superior. More of an adult/teen than they are. She has always had a high opinion of herself compared to others so I think it fits for her to say something like that.