"Next you'll say that digital is always better than analog"
Hmmm remind me again what the FCC is mandating regarding the phase out of analog broadcast TV in favor of digital?
"Likewise, if your cable box can separate the Y and C, convert analog to digital and send it over DVI to the tv where the tv will then do any processing like scaling, noise reduction, etc and convert it back to analog for display. I guesss all those conversions have no affect whatsoever, right? Wrong"
Again you don't seem to understand how cable companies transmit video or how digital TV's display video.
For digital cable the signal is sent as an MPEG stream not as an RF signal so the multitude of signal conversions that you are trying to portray simply does not exist at the level of the box. In fact if you feed a DLP TV from a digital cable box through a composite input you will get digital to analog conversion to make the MPEG signal composite, then you will get analog to digital conversion so that the TV can scale the analog image to its native resolution then the TV has to convert this back to analog for viewing.
The complaints that people have with "digital TV" and standard cable are related to these TVs being fixed pixel devices and natively progressive. For the most part content that is natively interlaced should be viewed interlaced.
"Why don't I notice any difference between component and DVI"
Discussed thoroughly on another thread on this site. Again garbage in is garbage out no matter what the connection.
"Why is it sometimes better to use interlaced mode from my dvd player even though I have it connected to a digital tv using component cables"
Only if you have a really cheap DVD player that doesn't deinterlace properly because remember none of the so called digital TV's that are fixed pixel devices can display interlaced signals. And how does this support your argument that composite is better than component
I asked for specific examples and the only one you could give was not even correct. Please stop misleading our other forum members. The proof is in the pudding. Have you actually seen these various connections and if so what type of cable box and television set did you use it on?
"Anyone who states as a matter of fact this type of connection is ALWAYS better than another is uninformed"
Again did you read the other posts on this forum or the excellent cable articles? Remember on this site physics and precise measurements always win so if you can find any article done with reputable methods supporting your contention of composite as a connection being better than component then I would be happy to give that a read.
Did you read the link I posted?