Why do some languages have grammatical gender?

Because grammatical gender is a noun classification system, and many languages use one — it is only confusing to English speakers because English lost most of its own.

What it actually is. Grammatical gender sorts nouns into classes that control agreement: which article, adjective ending, or pronoun must be used. It is a syntactic feature. The label "gender" comes from Latin genus, meaning kind or category, and originally had nothing to do with sex.

Why the assignments look arbitrary. German Mädchen (girl) is neuter, because the diminutive suffix -chen is always neuter — the rule is morphological, not semantic. French la sentinelle (sentry) is feminine regardless of who holds the post. Assignment often follows the noun's ending, its origin, or simple historical accident rather than any property of the thing.

It is not unusual. Roughly half the world's documented languages have some gender or noun-class system. Bantu languages have far more classes than two or three — sometimes over a dozen — sorting nouns by categories like humans, animals, plants, abstractions and liquids. Two- and three-gender systems are just the version Europeans are used to.

Many major languages have none: Turkish, Finnish, Hungarian, Persian, Mandarin, Japanese, Korean.

English used to have it. Old English had masculine, feminine and neuter with full agreement. It eroded between roughly 1100 and 1400, as unstressed endings weakened and contact with Old Norse — which had a different gender system for the same words — made the distinctions unreliable. Only pronouns survive.

Does it affect thought? Some studies find speakers describe objects using adjectives stereotypically associated with the noun's gender. Effects are small, sensitive to method, and have not always replicated.

Learning it: memorise gender with the noun, not separately, and learn ending-based patterns.