a story is about a character who wants something and has to overcome one or many obstacles to achieve it by making choices that affect the outcome. Thanos wants something and faces obstacles (driving the plot), but his choices are rendered meaningless due to his madness.
I suppose that's one interpretation. But, it is easily argued that every character with a spoken line in the movie wants one or more things. Each of the Avengers (and various associated people) collectively and individually want to stop half the universe from being killed, for example. And, in a typical story in Western heroic fiction, the protagonist is reacitve, rather than proactive. The antagonist creates the basic conflict and many of the obstacles. Without the antagonist, there is usually no story, because the protagonist is not challeneged.
You are actively choosing to interpret it with Thanos as the protagonist. As you note, the resulting story does not make much sense. Why, then, hold to that interpretation? If you turn it around, and note the varius superheroes are the protagonists, then the story comes out much more reasonably.
Second, animals need to be culled because they don’t have the human capability of reason to find solutions to the problems facing them.
Um, humans often don't have that capabilty. Rapa Nui (Easter Island) is a fine example - humans did to that island pretty much exactly what Thanos' people did to their homeworld - they consumed the resources until the island could no longer support them. The devastated the ecosystem. And they all died.
Just because a people have the ability to reason, in general, does not automatically mean that they (either individually or collectively) recognize a problem exists, have the understanding to formulate a solution that works, or the will to make it happen. Unless Thanos is unrealiable, there is proof that a culture can fail to beat this challenge.
Rational beings understand you can’t snap your fingers and make everything happy ever after.
No rational being (to our knowledge) has had access to the power implied by the Infinity Stones. It is perhaps better to note that one's ability to solve problems is limited by, among other things, one's ability to impact reality. Thanos' ablity to impact reality... was very large.