Operator precedence (bitwise '&' lower than '==')

You need to ask Brian Kernighan or Dennis Ritchie.
From this forum: http://bytes.com/topic/c/answers/167377-operator-precedence

The && and || operators were added later for their "short-circuiting" behavior. Dennis Ritchie admits in retrospect that the precedence of the bitwise operators should have been changed when the logical operators were added. But with several hundred kilobytes of C source code in existence at that point and an installed base of three computers, Dennis thought it would be too big of a change in the C language...

So, that might be a reason? I'm guessing since there are several layers of bitwise precendence (unlike relational comparisons) that it's cruft that's existed since...forever...and just was never corrected.

It doesn't make sense to Dennis Ritchie, either, in retrospect.

http://www.lysator.liu.se/c/dmr-on-or.html

&& and || were added to the language after | and &, and precedence was maintained for reasons of compatibility.

I don't have an authoritative answer as to why K&R chose the precedence they did. One example that makes a fair amount of sense would be this one:

if (x == 1 & y == 0) {    /* ... */}

Since this is the bitwise AND operator it uses a non-short-circuiting evaluation mode, as would

if (x == 1 | y == 0) {    /* ... */}

use the non-short-circuiting OR operator. This is probably why they chose to have the precedence group this way, but I agree with you that in retrospect it doesn't seem like a good idea.