호감 is 'having a good feeling" and 비호감 is opposit of 호감..
in korean ,"비, 부(불), 무 + 명사" is negative of 명사. usually ^^ not always..
cf) in, ill, anit, non, etc... in english
비호감 남자.. "a man who is not atrractive."
타다 is riding..
but in this case.. it means.. "being on some condition.."
so 최근에 비호감 타서 means..
he is on the '비호감 condition ' recently(최근에)
add) 잠수 타다
잠수 is diving underwater...
but in this case.. not showing on public..
철수는 요즘 잠수 탔어..
Chulsoo has not been showed recently... (Chulsoo is on the '잠수' condition)