I'm a big fan of training all muscles. Unless there is a solid reason why we're avoiding an entire muscle group (i.e., due to an injury, disability, doctor's recommendations, etc.), I'm likely going to create a training program that involves each muscle to some degree. No, just because you don't like training a certain muscle doesn't mean I'm going to encourage the neglect. This also doesn't mean every muscle will have it's own individual isolation exercise, but it does mean that we're not skipping calves.
The most commonly overlooked muscle groups are calves, hip flexors, adductors, biceps, triceps, and obliques. The shoe might not fit for all of these, but these are just to name a few. If you're a runner and you're reading this, I highly recommend you train your calves, hip flexors, adductors, and obliques regularly. (You use them in your sport!) If you're a runner and/or not a runner and you're reading this, I highly recommend you train all the muscles. (You use all of them in day to day life!)
If certain muscles are being avoided due to other reasons such as frequency of training, it would be worth seeing how you can maximize your session(s). For example, if you are strength training 1x per week, consider what your program could look like if you focus on completing compound movements or unilateral versions of compound movements weekly.
Here's a program starter example including most muscle groups:
1. Barbell Back Squat (glutes, hamstrings, quads, hip flexors, adductors, calves, back, core)
2. Single-Arm Floor Press (chest, triceps, anterior deltoid)
3. Single-Leg Deadlift (glutes, hamstrings, core)
4. Barbell Row (back, biceps, posterior deltoid, core)
Just in four exercises, you nearly hit 'em all. Of course, we'd still want to add mobility, accessory movements, and core specific exercises, but these provide a baseline.
So, to answer your question of "do you need to train every muscle group"?:
Need to? I suppose not, but I encourage it.
Want to? Absolutely, yes. Reap the benefits!
