Why does a an old projection TV show color on tweed jackets in B&W movies?

I have an old style projection TV, and I noticed while watching black and white movies on TCM, anytime there is a close-up of a tweed patterned jacket, color appears among the tweed. What is the reason for this?

Moiré patterns.

To add to Exapno Mapcase’s post:-

All TVs that take a “Composite” signal will do this to some extent – the NTSC and PAL standards were a way of cleverly fitting two different signals (colour information and luminance information) into the single space originally allowed for the luminance alone

  • it works surprisingly well, but it’s a bunch of compromises wrapped in a kludge - which is why “Component” (separate) or digital signals look so much better

With hard edges, say where the luminance changes abruptly from black to white, there is a lot of high frequency information in the luma signal. Some of this sneeks into the area of the composite signal reserved for colour and you see colour where there is none (some TVs are better than others at filtering the signal but all suffer) A strong pattern is made up of lots of such edges
(tweed is notorious for this and is strictly verboten for presenters, what interviewees wear is harder to control)

It’s not restricted to projection TV’s. I’ve noticed this on conventional CRT’s as long as I can remember.

You can notice on printers that don’t have black cartridges that the black areas don’t look black either. They use three colors put down to try and make black, but it’s not true black.

A moiré pattern also appears when videotaping a CRT monitor. If you are in perfect focus on the CRT, the moiré will appear over a lot if not all of the CRT. It moves around as the image moves.

Damned irritating. Frequently the solution is to go just slightly out of focus and the moiré drops away.