Learn Russian: Иногда я скучаю без семьи, но я люблю одиночество. - Sometimes I miss my family, but I love solitude.

Одиночество is a noun meaning "solitude" or "loneliness," and it is built from the root один (one/alone). While you are learning to use один to describe a person (like я живу один - I live alone), одиночество is the abstract concept of being alone.

Why does the speaker use скучаю без семьи instead of скучаю по семье?

Both phrases translate to "I miss my family." The construction скучать по plus the Dative case (по семье) is the most common way to express missing someone in Russian. However, скучать без plus the Genitive case (без семьи, literally "to be sad without") is also very natural and places a bit more emotional focus on the emptiness caused by their absence.

Is одиночество a positive or negative thing in Russian?

It can be either! In English, we often separate "solitude" (which can be peaceful) from "loneliness" (which is sad). Russian uses одиночество for both states. Because the speaker in this sentence says я люблю (I love), it is clear they enjoy being alone, so we translate it as "solitude."

What case is семьи in here?