Error with SEARCH formula

Hey, first time checking in here. I have a weird error that I'm quite not sure why it occurs

=if(and(isnumber(search({"1","2","3"},F2)),ISERROR(search({"site 1","site 2"},D2))),"True","False")

I have this piece that checks both ranking and if those sites aren't in the column next to it. The problem comes from the first "isnumber(search({"1","2","3"}" doesn't find the 2 or the 3 even though in the second search it has no problem of finding site 2? I'm not sure where the issue lies as it finds the first number but not any other.

Thanks in advance!