You may have heard that there are roughly 7 million men of working age that are not currently in the labor force — that is, not currently working or looking for work. The statistic has been produced in various ways using slightly different definitions by different researchers, but the most well-known is from Nicholas Eberstadt who uses the age cohort of 25-55 years old and gets about 7 million (in 2015). More recently and perhaps more prominently is from Senator JD Vance, and as with almost all issues he has tied this to illegal immigration.
The 7-million-men statistic is true enough, and if we limit it to native-born American men with native-born parents (I assume this is the group Vance is concerned about), we can get right at 7 million non-working men in 2024 by expanding the age cohort slightly to 20-55 year olds.
Why are these men not working? According to what they report in the CPS ASEC, here are the reasons broken down by 5-year age cohort (I drop 55-year-olds here to keep the group sizes equal, which shrinks the total to 6.7 million men):

By far the largest reason given for not working is illness or disability, which is 42% of the total for all of these men, the largest reason for every age group except 20-24 (who are mostly in school if they aren’t working), and it’s the majority for workers ages 30-54 (about 56% of them report illness or disability). Slightly less than 10% report “could not find work” as the reason they weren’t working, which is about 650,000 men in this age group (and are native-born with native-born parents). And over half of those reporting that they couldn’t find work are under age 30 — for those ages 30-54, it’s only about 7% of the total.
More men report that they are taking care of the home/family (800,000) than report not being able to find work (650,000). And a lot more report that they are currently in school — almost 1.5 million, and even though they are mostly concentrated among 20–24-year-olds, about one-third of them are 25 or older.
It’s certainly true that the number of working age men in the labor force has fallen over time. In 1968, 97% of men ages 20-54 had worked at some point in the past 12 months (that’s for all men regardless of nativity, which isn’t available back that far in the CPS ASEC). In 2024, that was down to about 87%. But even if we could wave a magical wand and cure all of the men that are ill or disabled, this would add less than 3 million people to the labor force, not nearly enough to make up for all of the immigrants that Vance and others are suggesting have taken the jobs of native-born Americans.