Why would a software engineer want to transition into product management?


Answer: There could be many reasons. Typical ones include:
First, they may want to increase impact in business or strategy decisions. A product manager usually owns the product's direction and roadmap, and also responsible for the end business results. 
Second, they may want to work more closely with customers and work with people in general. A product manager needs to talk to customers very often to really understand their needs and requirements. A product manager also needs to work across functions to push a project forward so they need to influence others.
Third, also note there are some commonalities between software engineer and product manager, they both build stuff and understand technologies, so for a software engineer it's usually easier to transition into product management than other functions because many skills are still relevant.