This is more of a question for sociologists, but we're all multidisciplinary these days, so here goes.

The problem with your question is that you assume secularisation is a sign of modernity and that the two go hand in hand. This isn't the case, however. Don't feel bad, though, because many prominent thinkers used to think this as well. Durkheim thought other institutions (civil religion, political religions, etc) would take over the functions of religion, while Weber thought the rationalisation of our society would decrease religion's relevance. During the sixties, two of the foremost supporters of this thesis were Peter Berger and Bryan Wilson - they both thought religion would lose influence and secularisation was inevitable. In the years following their publications on the subject, the thesis came under fire.

Arguments included the fact even in their European examples, private forms of religion were still very much present, that while church attendance was low, denominations still had large memberships and that the separation of church and state was incomplete. More importantly, they point out that instead of seeing Europe as being on the forefront of modernity and the US as an exception, it's Europe that's the exception. And not even the entirety of Europe supported the secularisation theory - areas like Spain, Italy, Eastern Europe, Ireland, etc are all highly religious. Opponents of the secularisation theory also point to the spectacular growth of religions like Islam and Pentacostalism. So not only is Europe an exception, when sociologists used it as an example of the theory, they took a far too simplified view of religion in the area and generalised way too much - to the point where it's not really an example of their theory at all.

Berger, for one, had to admit that 'the assumption that we lived in a secularized world is false.' He, like the other true believers of the theory, didn't give up on his belief that modernisation and secularisation are linked, however. But that means he needs a reason why secularisation didn't happen after all. He points at two things: some religions explicitly reject modernity (Salafism, for example), while others attempt to adapt to modernity (the Catholic Church, to an extent).

Others, like Rodney Stark and David Martin tried to come up with different theories of secularisation, which mostly emphasised the lack of competition on the religious marketplace as to why Europe was less religious than the rest of the world. Where European countries are often monoreligious, the other parts of the world have many religions on offer which compete to gain souls. The abundance of supply is supposed to create a greater demand as well. This approach has been criticised as ahistorical, seeing as countries like The Netherlands (to name just one) do have a great deal of religious competition, yet doesn't really stand out from its neighbours in terms of religiosity.

The secularisation theory is bunk, basically. That's an opinion, sure, but it's an opinion on very solid ground - as opposed to the opinion of those that believe in the theory. The evolution of religiosity in Europe isn't one of decline of religion, merely of transformation. And in that, it's not an example the rest of the world is following.

I'm sure someone else can fill you in on why the US is so religious, aside from all this theoretic stuff.