Because they wanted to be able to tap into German manpower to resist a potential Soviet invasion of Europe. A large, well equipped and well trained German army was a massive boost to Western Europe's defenses.

Source: Hans Peter Schwarz, 'Konrad Adenaur: from the German Empire to the Federal Republic'.

The USA saw Western Germany as being the front line for any Soviet invasion of Europe. They saw the latter possibility as not being in the US's interests. The problem is, the US didn't want to station a large peacetime military force in Europe if it could help it — it is expensive to do so and unpopular domestically. So they undertook many measures to try and get the Europeans to "aid in their own defense." NATO was part of this (though even then the European powers did not pull as much weight as the US), the re-arming of West Germany was part of this. As it was, there was a relatively small garrison of American troops in Germany that was meant to act as a "trip-wire" to any Soviet military action, meant to guarantee that the US would be pulled into any war that happened there, both to reassure European allies that the US wouldn't just abandon them, but also to deter the Soviets from trying it. But this was never seen as an ideal situation.