U-boats could (and did) sink quite a few destroyers and other D/C equipped escorts. And U-boats did fire fan shots at destroyers / escorts when facing attack and then go deep to evade D/C's. However, escort vessels were faster, more nimble, and more dangerous (i.e. hard targets) than the transports that were the true objects of the U-boats attentions - U-boats went out to sink transports, not warships, despite the propaganda value of the latter.

Attacking an escort also accomplished a few things that U-boats typically did not want to do: (1) it brought the U-boat closer to the escort, (2) it revealed (either by sight of the torpedo or sound of its high-speed propellers) the location of the U-boat to the escort, and (3) it placed the U-boat in a more vulnerable position, periscope depth, than if the U-boat immediately went deep to get under the priming depth of D/C's. In addition, if the destroyer / escort is charging the U-boat head on, the U-boat is faced with a very iffy zero angle on the bow "down the throat" shot at a fast moving target, with the likelihood that all the U-boat would do is waste its limited supply of torpedoes. All of these tactical realities generally weighed in favor of the U-boat evading, not attacking, a destroyer or other escort vessel.

The so-called acoustic or sound targeting to fire torpedoes was ineffective in WW2 because the technology hadn't been perfected (at least as to sub lauched torpedoes - the principle was realized in the "Fido" type homing torpedoes (Mk XXIV "mine") dropped by aircraft). The U.S. Navy doctrine adhered to early in the Pacific submarine war was to make acoustic launches, i.e., firing blind, by sound only. However, the doctrine was completely ineffective and was rapidly discarded in favor of visual launch procedures.

In sum, because the chances of success were not great, and the potential for damage or destruction significant, U-boats tended to avoid a direct conflict with a destroyer that was already on to them. In such situations they preferred to evade, rather than engage, their pursuers, and live to fight another day against their true targets: transports.