This is a pretty common thing. I have no particular insight into it, but I'll mention it anyway in case people don't know.
When you buy a bunch of asparagus, about 2/3 of it is usable. About 1/3 of it is thick and woody and not nearly as good. You could guess, but why guess when you can know?
Grab the spear in both hands. Stroke it.* Whisper dirty things to it.* Tease it.* Then, when it's least expecting it,** bend it until it snaps. The part at the end that snapped off is the woody... part. You can do one of three things with it. You can use it in a soup, because you can cook and puree it so that its woodiness melts away. You can carefully bag it, freeze it, and save it in anticipation fo making soup in the future. Or you can throw it out, because you're just going to forget about it and throw it out months later when you clean out the freezer. That's my preferred option.
Some people snap one asparagus, then cut the rest all at once to the length of the first snap. This is a step that will save you about two minutes, so if you only have a few days left to live, go for it. Otherwise, snap 'em all, because they'll all snap a bit differently.
* This step is not actually necessary.
** Asparagus, being a vegetable, will never expect this. So whenever you feel like it is fine.