There's quite a few feminine nouns that end in a consonant, there are masculine nouns that end in a vowel. This vowel/consonant thing isn't a strict rule. While it is true for most nouns, there's still a lot of exceptions. So you need to be careful and try to remember a noun with its gender
Are you asking why the word зустріч ends with a consonant and is feminine? I can't answer why, but some feminine words do end with a consonant. Not many, though.
For example, the word річ (a thing) also ends with a consonant and is feminine: Це моя річ. -- It's my thing.
"An appointment" marked wrong!?? But vowels(a,i,u,e,o) need "an", right? And then I typed "a appointment" on Google. And I found that other people want to know "a" or "an".
An is used before a (spoken) vowel sound. An appointment is grammatically correct, providing you pronounce the "a" in "appointment". Confusion happens with words like " hotel" which is pronounced "Hotel" or "otel". A hotel and an 'otel.