Learning to relax your antagonist muscle isn't just going to give you better control of your strength; it'll give you better peace of mind. Your overall mobility will improve by leaps and bounds.
Imagine this scenario: you are helping someone to move furniture into their home. You reach the couch and ask the person to lift one side as you lift the other.
As you begin to lift, the other person pushes your side down. You lift harder, yet the other person pushes down harder. You probably won't lift it this way, and may leave a physical, lasting reminder for your friend not to do so again, or simply vow not to help them move.
Nevertheless, when you train without a proper sense of muscle control, this is exactly what you are doing to yourself; you're pushing the couch down as you're trying to lift it.
Unless you can identify the problem (What is pushing the couch down? How do I stop it?), you'll never be as efficient with your strength as you could be. The problem is this instance is your antagonist muscle.
An antagonist muscle is a muscle that acts on or against the muscle movement that you try to perform. If you wanted to do a bench press, your back muscles and biceps are your antagonist muscles. When you do a bench press while mentally wound up, you'll perform the lift with tension all around your body.
This tension in your antagonist muscles will work against your lift (your triceps try to push the weight while the tension in your biceps tries to pull it down).
Consequently, while you may have the strength to perform a 315lbs bench press, you're reduced to lifting no greater than 275 when you don't relax these muscles. You may get stronger, but you'll never utilize your full strength efficiently while your antagonist muscle “friends” are pushing down on the weight that you're trying to lift.
This really applies with one of the more advanced bodyweight exercises: the one-legged pistol squat. Well, squats in general too. Most people have the overall strength to perform one legged pistol squats for reps, but their hip flexors don't have the strength to support the extended leg, and antagonize the movement. Or, they don't activate the glutes enough to properly perform the movement.
Squats are a fantastic movement to work out, but it's really easy to plateau in your squats. Why? Antagonist muscles. Most people who squat are quad-intensive; these people have pretty powerful quadriceps to drive their squats up.
The problem here is that squats require ankle mobility and glute strength. You have to train your antagonist muscles (glutes, tibialis, hip flexors, etc.) to really draw out the power you want for your lift.
Another problem is that squatting with just the strength of your quads is a formula for knee injury. Get that butt back and use your hips, not just your quads, to get that weight up.
There is a process that you can take to systematically reduce all of your wasted energy and “lift the couch”. The system is muscle control, and learning it is invaluable for displaying your true strength potential.
If that doesn't appeal, I recommend bodyweight movement exercises. Honestly, big weight lifts are great for building strength, but if they aren't taught correctly, the lifts can mess with the overall balance in the body.
Doing things like bear crawls or alligator walks, for instance, is great for working all muscles in the body, including antagonist muscle. By learning to use the whole body as one unit, you develop better joint mobility, but also strengthen and relax those antagonist muscles for when you do go try out those big lifts.
There's a great video on different types of movement training that I invite you to check out below.
Please put any thoughts, questions, or feedback here and I'll respond as soon as I can.