Many people are sympathetic to foundationalism. In some respects, they think it accords with our common sense. Like this, for example. Because I'm looking at a Christmas tree in my house that has been up now past Christmas, because I have this belief, and this belief looks to me to be caused by the most immediate experiences I'm having, something like foundationalism must be true. I must have at least some basic beliefs.
Nobody is going to doubt that my perception of the Christmas tree is immediate to me. But what they very well could doubt is that any subsequent beliefs I have about the Christmas tree, even that I see it, could be supported by any number of beliefs connected to my perception of the tree.
One of the objections to any alternative to foundationalism, according to the SEP article on epistemology, is the regress argument. The argument is something as simple and stupid like: But if I need to give a reasons for my belief in terms of another belief, don't I need to give a reason for that belief in terms of another, and in terms of another, blah ditty blah blah? Therefore, foundationalism is true.
Even assuming that it somehow follows that foundationalism is true from this half an argument, the premises don't work. Like, the assumption is that each belief needs another belief to be justification for another. So, for example, B1 (belief 1) justifies B2 which justifies B3, and so on. But think about how explanation works, both formally and informally. Once we hit a certain point in our understanding, we just accept that there is no explanation past some such beliefs or we give a circular justification. That likely means that something like coherentism is true. There is always possibility for other beliefs we have that are reasons for the immediate beliefs we have, and this all go together in a kind of chain, it seems.
Another argument for foundationalism is that the alternative coherentism does not allow the possibility that our beliefs are actually in contact with the world. Foundationalism as a position does, so we're supposed to accept that. But that's malarkey because if you accept that idea that it's impossible to make the world in its totality intelligible with one's beliefs, then the most we can hope for is having the best beliefs in light of the best and most explanatory theories, formally and informally. Nothing wrong with that. Are minds are not designed such that we're guaranteed complete understanding of the world, you know.