While I sympathize with you, I find it hard to answer your question.
On the one hand, as phrased you are asking whether an emotional response is valid. Well, it is not really for anyone other than you to determine the validity of your emotional responses, and in all of my experience, "That is not a valid emotional response" is rarely a useful piece of advice. On the other hand, your question is pitched in a certain level of generality, but understanding why you feel the way you do seems to require knowing more particulars of your situation than you have disclosed.
But let me say what I can and what might be helpful:
The way I see it, a paper has a certain lifespan in terms of being read and cited. Once it has been generalized, that lifespan is in most cases over. If someone wanted to understand a theorem, they would probably look for the most general version. Of course, this does not always apply, for example if the work represents a milestone of some kind. One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art).
Since you speak of "theorems," I gather you are working in mathematics. (This is corroborated by one of your other questions, where you identify yourself as working in applied mathematics.) I am also a (pure) mathematician, and the way you describe "obsolescence" is neither the way I think about mathematical results nor how I have heard other mathematicians talking about them. Maybe it is quite different in applied mathematics, but in pure mathematics there is not any prescribed lifespan on papers being read and cited. To try to quantify this, I just looked back over my last 10 accepted papers, and for each one identified the earliest cited paper. Of these ten papers, the latest one was published in 1976. (Moreover the 1976 paper came from a five page note with only a few citations.) In other words, in all of my recent papers I have cited papers that are more than 40 years old, and in fact usually older than that. In my department I have many colleagues who are 10-20 years older than I but who have a similar number of publications to me (publication pressures have risen in recent years). Most of these colleagues have higher total citation numbers than I do -- I think because their papers from 10, 20, 30...years ago continue to be cited. My most highly cited works were published in 2013, 2005, 2006, 2010 and 2003, respectively.
[Moreover, in mathematics, citation numbers are not (yet!) the ultimate metric of academic worth. Papers written on finite graphs tend to get more citations than papers written on admissible representations of p-adic groups because there are more people working on the former and many more people who know what the former are. I think most mathematicians realize this.]
So I have to wonder about the specific situation you are describing. In a different question, you mention a colleague of yours who worked on the same problem as you and came up with a result that was in some but not all ways more general, and then you published at least two papers together. I don't understand why this would "short circuit" your citations. Now you describe a situation in which your colleagues are working on generalizing one of your results, apparently without any new ideas. In this latter situation especially, I would expect that if they publish an improvement of your results using ideas essentially due to you, then that should augment your results in every way (including citations), not detract from it. (You are aware that senior mathematicians do this all the time, and the work of their students is usually viewed as an extension of their own work, I trust?)
Then you say:
I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).
If it gets to the point of an independently published generalization of your work, then I don't see how it makes any difference whatsoever if your coworkers were involved. However, before that happens the fact that it is your coworkers puts you in a much better situation: namely, in the worst case you have much more advance knowledge of what they are working on and can plan accordingly. In the best case you can pursue a collaboration with them in whatever way seems best to you.
If I may take a guess -- are you perhaps most upset by the fact that your coworkers have chosen to pursue these generalizations of your work without your involvement, so that they seem to be competing with you right under your nose? I could understand why that would be upsetting. If you feel that way, I think you should be much more proactive about collaborating with them.