Quick Question about 始まる vs 始める

Question

In today's Japanese class, my teacher said "私が始まる" instead of what I had expected to hear which is "始める"　to mean "I will be the one to start". I'm sure of that meaning because of the obvious context.

"私が始まる" was kind of disorienting because if I'm not mistaken I know generally (Except verbs that are like 歩く、走る、寝る、etc) that intransitive verbs in Japanese typically take "Something" as the subject as opposed to "Someone" so it felt like 私 was "thingified" or something like that. This could have also been just simply an unintentional ミス from my teacher so I don't want anybody reading this getting confused. But if it isn't, kindly go into detail as to why.

Thanks in advance.

Edit: I posted a now-deleted answer paraphrasing what @aguijonazo said in the comments since @naruto 's answer is the same as well as adds a few nice points. Full credit goes to them for helping out.

Edit(2): @aguijonazo's response to my now-deleted answer as more clarification for what he/she said: "I meant the speaker sees him/herself as a show or something as in "Now the show begins."

Answer 1

私が始まる would make perfect sense as a rhetorical sentence meaning "This is the beginning of myself" or "My (true) life starts here". It might be called a metonym of life. I used this lyrics search and found 4 Japanese songs that literally contain 私が始まる:

But if your sentence is supposed to mean "I am the one who will start it" (where "it" refers to some event such as a game, a program), you must say 私が(それを)始める using the transitive version of 始める.