It is not just GLP-1 one drugs that cause muscle mass loss to be a problem. When you lose weight by any method (e.g. caloric deficit, bariatric surgery etc.) you will lose both muscle as well as fat. Exercise and dietary choices while losing weight (protein) can lessen the effect of muscle loss but the reality is that anytime you lose weight you will lose both fat and muscle in some proportion. The result is that your lean body increases, which I would argue is a good thing.
Here is an article from NBC along with several quotes:
"When we look at weight reduction from any intervention, about one-third of the weight we lose tends to be lean mass, and that can be problematic,” said Dr. Jaime Almandoz, an associate professor of internal medicine in the Division of Endocrinology at UT”
… “That’s why we try to emphasize slow, consistent weight loss rather than quick weight loss, where you’re more likely to pull from your energy stores” in muscle, said Dr. Jonathan Purnell, an endocrinologist and professor of medicine at the Oregon Health and Science University Knight Cardiovascular Institute in Portland. Purnell has done consulting work for Novo Nordisk, according to the Centers for Medicare & Medicaid Services.
“It’s also a function of how low you go,” he said. “Once you enter into the healthy BMI range, you’re more likely to be pulling from the lean stores.”
Despite concerns about muscle mass loss, at the end of the dramatic weight loss period, people may actually have a healthier body composition, that is, the ratio of lean mass — especially muscle —compared to fat.
On ways to not lose too much muscle mass:
There are ways to mitigate lean mass loss during weight loss ...said Dr. Juliana Simonetti, co-director of the Comprehensive Weight Management Program at the University of Utah in Salt Lake City.
...One way is to make sure you’re eating enough protein, which can be difficult to do while using weight loss drugs. Protein is the building block of muscle; without enough of it, muscles aren’t able to build and repair themselves
...Exercise, specifically resistance training, is also a critical part of maintaining muscle mass during weight loss, she said.
"People are best convinced by reasons they discover themselves"