In men, testosterone declines slowly from around age 35 to 40 at a rate of 1 to 3% per year, which can coincide with fatigue, loss of libido and mood complaints. This process differs fundamentally from the female menopause, and whether the complaints are fully explained by hormonal changes has not yet been conclusively proven.
Yes, something like a 'male menopause' does exist, but it is fundamentally different from the female menopause. From around the age of 35 to 40, testosterone levels in men decline by approximately 1 to 3 percent per year. This gradual process is called andropause, or sometimes 'late-onset hypogonadism' (PMID 21058750, 8243411).
The key difference from the female menopause is that in women the ovaries abruptly and completely cease functioning, whereas in men the process is a slow, creeping decline that unfolds over decades. Men also remain fertile well into old age, although sperm production and sperm quality do gradually decrease (PMID 8243411, 12574711).
Some middle-aged men report complaints that resemble those of the female menopause: fatigue, reduced libido and mood changes. Whether these complaints are caused entirely by the hormonal decline is, however, a matter of debate. An association has been demonstrated, but there is no evidence of a direct cause-and-effect relationship (PMID 12574711).
Work-related factors also play a role. Psychological stress, heavy physical strain and sleep problems are associated with more severe complaints, as shown by a systematic review of 9 studies (PMID 34639376). Stress and illness can moreover accelerate the age-related decline in testosterone production in the testes (the so-called Leydig cells) (PMID 8243411).
An additional point of attention is that couples may simultaneously be dealing with hormonal changes: the man with andropause and the woman with menopause. This can affect the sexual health of both partners, and treating only one partner may then be insufficient or even counterproductive (PMID 29371146, 37932239). Finally, the decline in testosterone and growth hormone also has a modest negative effect on skin and wound healing, although this relationship remains associative for the time being (PMID 20480124).
The claims are based on a mix of review studies, a systematic review and older primary studies. The evidence for the hormonal decline itself is reasonably solid; the evidence for a direct causal relationship between that decline and complaints is weaker and primarily associative.