Learn Turkish: Yağmura rağmen dışarı çıkıyoruz. - Despite the rain, we are going outside.

The postposition rağmen (despite / in spite of) always requires the word before it to be in the dative case (-a or -e). Since the last vowel in yağmur (rain) is a back vowel, it takes -a, making it yağmura rağmen.

We are going to the outside, so why isn't it dışarıya çıkıyoruz?

Direction words like dışarı (outside), içeri (inside), and aşağı (down) can take the dative case (dışarıya), but they usually drop it when placed right next to a verb of motion like çıkmak (to go out). Saying dışarı çıkıyoruz is the most natural and common way to phrase it in everyday Turkish.

Can I use rağmen to say "Despite raining" instead of "Despite the rain"?

Not with this exact structure. Rağmen paired with a simple dative ending only works for nouns and pronouns. To say "despite raining" (an action), you have to use a special verb suffix to turn the verb into a noun phrase, which you will learn in a more advanced lesson. For now, stick to nouns!

How would I change this sentence to say "Despite that, we are going outside"?