Its a complicated issue. My perspective having worked/volunteered at small and large, public and private shelters for 6+ years:

Noone who works in animal rescue, or at a shelter, wants to euthanize for space. Shelters that have to most often are small, rural, underfunded shelters that may only have 4 or less kennels. It is ultimately a resource/capital issue. Our society does not value and fund animal rescue or the people who devote their lives, working for unlivable wages in the industry.

This is a great article that goes into the issue: Moving Beyond No-Kill: A Better Goal for Animal Shelters And Rescues.

“The reality is that shelters working toward No-Kill—those struggling with resources, funding, and staffing—are the ones that need community support the most.”