Should I convince my advisor that thesis work is not finished yet? I am a third-year Ph.D. student in computer science. I have finished all course requirements and I work full-time as a software engineer at a FAANG company. I am doing my best trying to balance time between work and school. But today I had a meeting with my advisor and he said by the end of summer he expects me to wrap up all my thesis work.
Basically, I did

One year of study the research material and taking graduate-level courses to study the problem
One year of research to understand the problem and come up with the solution
One year of solving the problem, coding, and showing my method worked

What is remaining is writing a paper and defense.
My advisor is very strict and I am kind of surprised he said that. I don't feel like I have accomplished anything yet and there is more to the problem. Should I try to explain the work is not finished yet? Or maybe he is getting tired of me and wants to focus on other problems.
Working full-time as both a software engineer and a Ph.D. student is unsustainable. If writing a thesis based upon the results you have is likely to suffice (speak to fellow students, read theses of prior students, speak to your advisor), I'd suggest you take that route. Reduce your workload to something more sustainable. Your thesis needn't be your best work; your thesis need only get you a PhD. Graduate, pursue the next step.