Learn Spanish (Spain): Yo no soy el profesor.

In Spanish, making a sentence negative is very straightforward: you just put no right in front of the verb. While in English you say "I am not", the Spanish structure is closer to "I not am" (Yo no soy).

Do I always need to include Yo in a negative sentence like this?

No, you can perfectly say No soy el profesor. Because the verb form soy is only ever used for "I", the word Yo (I) is optional. Spanish speakers usually include it when they want to emphasize exactly who they are talking about, like saying "I am not the teacher, she is."

I've learned that we don't use articles with professions in Spanish. Why is el used here?

It depends on the meaning! If you just want to state your occupation, you drop the article: No soy profesor means "I am not a teacher". However, by adding el (the), this sentence specifically means "I am not the teacher" (referring to a specific teacher, like the one in charge of a particular classroom).

Why do we use soy here instead of the other "I am" verb, estoy?

Soy comes from the verb ser, which is used to talk about identity, core traits, and professions. Since being a teacher is part of someone's identity, we use soy. The other verb, estar (where estoy comes from), is used for temporary things like feelings or physical locations.