I was pursuing Ph.D. at a certain institution, let's call it X. After I started working, my experiments would fail repeatedly. My supervisor started calling me incompetent in the first two months of starting my Ph.D. Only later did I know that my experiments were failing due to some uncontrollable factor that I was not initially aware of. Later, I found research articles to support my argument and told about the same to my supervisor. Now, he was pressurizing me to do something unethical and I refused, quit the program after one year. Now, I am planning to pursue Ph.D. somewhere else, probably in the USA. Should I tell the admission committee and prospective supervisor what I went through and why did I left first Ph.D. programme?
There are a lot of reasons that people want to change programs. You don't need to have a justification to want to join the program of Y rather than X. You are seeking better guidance and a more supportive atmosphere, but you don't even need to stress that.
Don't however, make accusations about individuals.
In your written application materials, just list the existing program. In your statement of purpose focus on that (SOP), not on the past. If there is a well respected potential advisor or group sharing your interests, focus on that. Make it forward looking and positive.
If you are asked during an interview you can say that you were a poor fit for the other program and had some ethical concerns with behavior there. You don't need to go into detail, and, again, shouldn't make accusations.
In the US, most graduate schools will ask for a transcript from every school you ever enrolled in. So, they will know that you were in this program and left it without a degree. Given this, it is a good idea to concisely, neutrally, and optimistically describe the circumstances under which you left in your statement of purpose. For example, rather than saying unethical, you may want to say "I did not feel his suggestion of X was appropriate."