Squat heavy, the story goes, and testosterone floods your bloodstream. Everything you train that day grows faster. Skip legs and your arms stall, because you haven't given them the hormonal environment they need.
It's a convincing reason to do something you were probably trying to avoid anyway.
Hard leg training can briefly raise testosterone. The useful question is whether chasing that rise helps you build more muscle. The studies don't give us a good reason to programme around it.

What happens after a leg session?
In one experiment, eight young men trained an arm on its own on one occasion. On another, they trained the other arm, then did a large amount of leg work. The arm exercise was the same, but adding legs raised testosterone, growth hormone and IGF-1. Arm training alone didn't produce those rises.
Both sessions increased muscle protein synthesis, the process of making muscle proteins. The researchers found no extra increase from the higher-hormone session. Everyone received 25 g of protein after the arm exercise, so this was a test of the response with protein available. West et al., 2009.
That helps answer the immediate question. It doesn't tell us everything about what happens after months of training.
Did the extra hormones produce bigger arms?
A second study followed 12 young men for 15 weeks. Each trained one arm alone and the other with the same arm exercise followed by leg training, on separate days.
Arm muscle cross-sectional area increased by 12% in the lower-hormone condition and 10% in the higher-hormone condition. There was no statistically significant difference in growth, and the extra leg work didn't produce a strength advantage for that arm. West et al., 2010.
That does not mean leg training reduced arm growth by two percentage points. The difference could be chance. Nor does a study of 12 people prove that the true effect is exactly zero. It found no detectable benefit from repeatedly creating the larger hormone response.
Using each person's arms for comparison reduces differences in genetics and training history. It's still an exercise experiment, rather than a perfect isolation of testosterone: adding leg work changes more than hormone concentrations.
A larger study followed 49 resistance-trained men through 12 weeks of training. Their post-exercise hormone rises were not significantly related to their gains in muscle size or strength. This was a test of whether the rises predicted results, rather than another legs-versus-no-legs experiment. Morton et al., 2016.
What about the study that found a benefit?
There is a contrary result worth including. Rønnestad and colleagues studied nine people for 11 weeks. They found greater relative biceps-curl strength gains and some favourable muscle-size results when an arm was trained after leg exercise.
Both conditions increased overall arm muscle volume. The reported advantage was more specific than “legs made the whole arm grow more”. The order also differed from West's studies: legs came before the arm exercise. Rønnestad et al., 2011.
That leaves a small, mixed body of evidence. It doesn't justify promising bigger arms from a squat-induced testosterone rise. My practical recommendation is to judge a programme by your progress and recovery, rather than the hormone response it might produce.
Does this mean testosterone doesn't matter?
No. These studies concern brief, naturally occurring changes around exercise, mostly in healthy young men. They don't establish that testosterone deficiency is harmless, or that changing someone's testosterone for a prolonged period has the same effect as a short workout response.
They also don't show that your usual resting testosterone has increased. A blood sample taken just after training and a properly timed diagnostic blood test answer different questions.
If you have persistent symptoms that could reflect low testosterone, discuss them with a clinician. Diagnosis requires compatible symptoms and consistently low results, usually confirmed with repeat morning, fasting tests. The cause matters: some forms are reversible, while others need specific treatment. Adding another leg session isn't a substitute for that assessment. Endocrine Society guideline, EAA guideline on functional hypogonadism.
So should you train legs?

Yes, if stronger or more muscular legs are part of what you want from training. You can make that decision without needing a hormone-based explanation.
For arm growth, keep track of the arm training itself: what you're doing, whether you're progressing and whether you can recover from it. There's little practical value in adding exhausting leg work solely to chase a testosterone spike.
Train legs as part of a programme you can sustain. Your progress over the next few months will tell you more than your testosterone immediately after a set of squats.