Why does TZ=UTC-8 produce dates that are UTC+8?

The reason is that TZ=UTC-8 is interpreted as a POSIX time zone. In the POSIX timezone format, the 3 letters are the timezone abbreviation (which is arbitrary) and the number is the number of hours the timezone is behind UTC. So UTC-8 means a timezone abbreviated "UTC" that is −8 hours behind the real UTC, or UTC + 8 hours.

(It works that way because Unix was developed in the US, which is behind UTC. This format allows the US timezones to be represented as EST5, CST6, etc.)

You can see that's what's happening by these examples:

$ TZ=UTC-8 date +'%Z %z'
UTC +0800
$ TZ=UTC8 date +'%Z %z'
UTC -0800
$ TZ=FOO-8 date +'%Z %z'
FOO +0800

The ISO -0800 timezone format takes the opposite approach, with - indicating the zone is behind UTC, and + indicating the zone is ahead of UTC.

Whenever you specify a timezone in the format of +/-00:00, you are specifying an offset, not the actual timezone. From the GNU libc documentation (which follows the POSIX standard):

The offset specifies the time value you must add to the local time to get a Coordinated Universal Time value. It has syntax like [+|-]hh[:mm[:ss]]. This is positive if the local time zone is west of the Prime Meridian and negative if it is east. The hour must be between 0 and 23, and the minute and seconds between 0 and 59.

This is why it appears to be the reverse of what you expect.

Why?

Because POSIX requires it.

If preceded by a '-', the timezone shall be east of the Prime Meridian; otherwise, it shall be west (which may be indicated by an optional preceding '+' ).

So, this will give time near^[1] Los Angeles (with any 3 letter label for time zone text):

$ TZ=ANY8 date "+%Y-%m-%d %H:%M:%S %Z%z"
2016-04-23 10:47:12 ANY-0800

$ TZ=GMT+8 date "+%Y-%m-%d %H:%M:%S %Z%z"
2016-04-23 10:47:12 GMT-0800

And this should give the time near Shanghai, China or Perth, Australia:

$ TZ=ANY-8 date "+%Y-%m-%d %H:%M:%S %Z%z"
2016-04-24 02:47:12 ANY+0800

$ TZ=CST-8 date "+%Y-%m-%d %H:%M:%S %Z%z"
2016-04-23 02:47:12 CST+0800

^{[1] Near because there may be some DST (Daylight Saving Time) in effect that shift the actual "local time".}