Learn Spanish (Latin America): Sin embargo, soporto esta monotonía agobiante cada día. - However, I tolerate this exhausting monotony every day.

Soportar is a classic false friend. It means to put up with, tolerate, or bear something (like an exhausting situation). If you want to say "support" in the sense of backing an idea or a person, you should use apoyar. For financial support, use mantener.

What is the root of the word agobiante?

It comes from the verb agobiar, which means to overwhelm, oppress, or weigh down. If you want to say you feel overwhelmed, you can say estoy agobiado or estoy agobiada. In this sentence, the adjective agobiante describes the monotony as suffocating or exhausting.

Since this lesson covers cualquiera, could I say un día cualquiera instead of cada día here?

They give completely different meanings. Cada día means "every day" or "each day" (a repeating daily cycle). If you changed it to un día cualquiera, the sentence would mean "However, I tolerate this exhausting monotony on just any ordinary day," which loses the intended meaning of enduring it on an everyday basis.

Is there a difference between cada día and todos los días?