The title of the post is a summarized answer to your question of why Cydia isn’t working the way you expect it to work with your iDevice having a tethered iOS 4.2.1 jailbreak. According to MuscleNerd, the tethered jailbreak is also the reasons for Cydia having a white icon and Safari crashing.

Here’s the lengthy and informative explanation from the iPhone Dev Team:

The notion of a “tethered” jailbreak is pretty new to many people, so here’s a quick rundown on what to expect:

  • If you’re on an iPhone3G, old-bootrom iPhone3GS, or non-MC ipt2g, life is easy. redsn0w installed an untethered jailbreak and so nothing below applies.
  • “Tethered” does not mean you cannot boot at all without PC/Mac assistance.  If you have not installed any tweaks that hook into important programs like SpringBoard or CommCenter, your device will actually boot. However, jailbreak programs like Cydia won’t work (and Cydia may still have a white icon).  Also, certain built-in apps that had to be moved by Cydia will fail (Safari being the most noticeable example).
  • If you’ve installed MobileSubstrate tweaks that hook into SpringBoard or other important programs, your boot will actually fail (you’ll get stuck at the Apple logo).  You need to use redsn0w to “Just boot tethered right now”.

The iPhone Dev Team have been hyperactive ever since the iOS 4.2.1 went live. They rolled out redsn0w 0.9.6b4 within 24 hours of the firmware release which brought tethered/untethered jailbreak for iOS 4.2.1 compatibles iDevices and are now planning on rolling out iOS 4.1 unlock during the course of this week.

Guide to jailbreak iOS 4.2.1 using redsn0w 0.9.6b4 can be found here.