Cool, in Italian it's the same structure, dimenticare DI qualcuno. Ironically, i keep forgetting the Hebrew word for forget over and over again :D
I think it's because they there too many words at us in this section for the Hebrew. I struggled, and still do, with a few words.
I have to guess that this is one of those awkward verbs that need a preposition because they can.
To explain the preposition: in classical Hebrew this verb could take מן, although it often did not. It does in תהילים (Psalm) 102:5 כי שכחתי מאכל לחמי, but does not in Ps 9:13. Some verbs take prepositions. Another verb that takes מן is מבסוט מ, "pleased with." Verbs of fear and distancing take מן, whereas verbs of giving and communicating usually take ל (Glinert, Modern Hebrew, 61). Certain verbs take ב such as לגעת ב, תומך ב, צופה ב. Sometimes there are additional curveballs, such as when לקרוא ב "to read" but לקרוא ל "to call." It's a good idea to acquire a dictionary that indicates the preposition that tends to go with a particular verb. If your hand dictionary does not, then you have to put the preposition tendency in by hand, as I am doing with my outdated Dov Ben-Abba (1977). Prepositions can be among the hardest aspects of language learning.
DL accepted "He is forgetting me", so they would very likely have accepted "He forgets me" also.