"School is starting next week."
to start has a pair of transitive/intransitive verbs in Japanese. to make it simple, transitive verbs take on direct objects, while intransitive verbs do not. 始める is transitive whereas 始まる is intransitive.
先生が授業を始めます。the teacher starts the class.
授業が始まります。the class starts.
note that 授業 is attached with the direct object particle を in the 1st sentence, and with the subject particle が in the 2nd.
I'm getting really annoyed with how inconsistently the course expects me to use the te-form for activities in progression. Why do the notes teach it to begin with to present me with hundred examples where they give me a present progressive sentence in english and then expect me not to use the te-form as if they just want me to do it incorrectly?
I suppose that it is pretty confusing. Since the sentence says "next week," it should be clear that the "starting" is not describing an action already in progress but is actually describing an activity that will start in the future (next week, not something already begun). はじまる is a word that's often confusing in this way.
"will start"/"is going to start" are also acceptable ways to phrase the English sentence in this case.
It sounds a bit strange to me on its own, having "next week" as the topic.
I think it would make sense to say it in a context where you're planning when to meet, such as: 来週は学校が始まりますから、午前は無理ですね。(School starts next week, so we can't meet up before noon.) And then suggest this week, before school begins.
According to some grammar material I've read (http://www.guidetojapanese.org/learn/grammar/particlesintro), this sentence should rather have は instead of が, both are correct tho Is it so?