It is a bit of a fetish. As far as we currently know, there is no reason to believe that using the first four bytes of the HMAC output would not be equally secure.
However, lack of reason to believe does not imply that nobody believes. Some people "feel" that systematic truncation may help the attacker in some completely unspecified way. With a lot of handwaving, one might argue that the dynamic truncation will make the task a bit harder for an attacker who tries a brute force attack on the secret key, with the help of dedicated FPGA or ASIC:
Since all 20 output bytes may be needed, the attacker must compute a complete HMAC/SHA-1; if only the first four bytes were used, then a dedicated unrolled circuit might skip a few steps in the last SHA-1 rounds (we are talking about an optimization of, at best, 3% here).
The "dynamic truncation" implies some kind of data-dependent lookup, which can be expensive in hardware area (again, this is mostly negligible with regards to all the 32-bit adders in SHA-1).
But these are not, really, good reasons. So the main point of the "dynamic truncation" is to be some kind of crypto voodoo that may awe the neophyte, and thus possibly help in acceptance. Specifying a good algorithm is not enough; implementers must also be convinced to use it, and, for that, some magical-looking gestures can play wonders.