Learn Finnish: Koira kieltäytyy juoksemasta metsässä. - The dog refuses to run in the forest.

Because of the main verb kieltäytyy (refuses). In Finnish, the verb kieltäytyä requires the action you are refusing to do to be in the third infinitive elative form, which ends in -masta or -mästä. You can think of it literally as the dog refusing 'from running'.

How do we build juoksemasta from the dictionary verb juosta?

First, find the strong verb stem. Juosta is a type 3 verb, and its stem is juokse-. Then, add the third infinitive marker -ma-, followed by the elative case ending -sta. Together this makes: juokse- + -ma- + -sta = juoksemasta.

If the dog was refusing a physical thing instead of an action, would it still use the -sta ending?

Yes! The verb kieltäytyä always demands the elative case (-sta/-stä). If refusing an action, you use the third infinitive -masta/-mästä. If refusing a noun, you just attach -sta/-stä directly to the noun's stem (for example, koira kieltäytyy ruoasta means 'the dog refuses the food').

Since the dog is refusing, why do we use metsässä (in the forest) instead of an 'out of' or 'away from' location case?