Welcome to the club of those who are confused by peronism, it's a very crowded club. It doesn't help that there are left wing and right wing peronist parties and that even Argentinians have a hard time explaining it to outsiders.

Many people conceive Peronism as a sort of "soft fascism", but that doesn't explain why peronism is so popular, why it survived after the death of Perón and why it dominates argentinian politics under different shapes. I also can't fully understand peronism (the closest thing I can think of is Gaullism, but on steroids), but as I understand it, I think the main reason why peronism is so popular is that in its essence, peronism vaguely embodies a few ideals (social justice, economic independence and political sovereignty) that most argentinians seem to agree on. Juan Perón itself predicted that the way of achieving the ideals of peronism would change, but the ideals themselves would not:

There are things that are permanent such as an ideology. We already do have an ideology, and, for a long time, for a long time, that will be cast into stone. Hoisting the flags of social justice, of economic independence and of political sovereignty, that is very difficult because they are permanent things. Instead, the doctrines, that are the form of execution of that ideology, change according to the circumstances and evolve with the evolution itself. The generational change tries to renew within time those forms of execution"

I recommend you to ask in /r/argentina if you don't get better answers here.