"if we are using proper coax assembled properly and we tune the antenna properly by adjusting its stinger and we get an acceptable match why does that match sometimes change for some folks on their meters when they change to a different length of coax if it is also in proper condition ?"
Because if you adjust the length of the antenna for best match with a particular length of coax, you are doing two things. First, you are also adjusting that antenna's resonance since length determines that. An SWR meter doesn't know what resonance is, it can't measure it, it can't tell you anything about resonance.
That SWR meter can only tell what the gross impedance match/mismatch is. If you are doing that reading from the transmitter end of the feed line, then you are actually reading the combined impedance of the feed line -AND- the antenna. That meter can't tell the difference between just the antenna's impedance, or just the feed line's impedance, it can only tell you what the combined impedance of both antenna and feed line is. So, if you change that feed line's length, you've also changed the combined impedance of the feed line and the antenna. It will -always- work that way UNLESS the antenna's input impedance is the same as the characteristic impedance of the feed line. That's why it's always better to do that antenna impedance matching AT the antenna rather than with the feed line. If the antenna is really 50 ohms and no reactance, which will mean resonant AND an SWR of 1:1 (or close), the length of the feed line makes no difference. You've eliminated the feed line as a variable.
Since it's sort of difficult to put that SWR meter at the antenna's input in most cases, you can use a particular length of feed line that is 'invisible' to RF at the frequency of use. That particular length of feed line is an 'electrical 1/2 wave length'. Which is where the velocity factor of the feed line comes into play. That E1/2 wave length not long enough to reach the antenna? Use whole multiples of that length, same difference as far as RF is concerned, it's like it really isn't there and the meter is hooked directly to the antenna's input.
So how do you find the right length for that "invisible" electrical 1/2 wave length of feed line? You have two choices. Do the math, or, use a meter that can tell you how long it should be. That meter will never be an SWR meter. Sorry, it just can't do it.
If it ain't one thing, it's another! Ain't it??
- 'Doc