Can I tell my PhD supervisor honestly why I want to leave him

My suggestion is that you talk about all of the reasons you are moving to the other university, as opposed to leaving the current one. These reasons could be to do with relationships (e.g., family) or future opportunities (e.g., a postdoc) or being paid whilst you are currently unpaid. If you have to give a reason why you are leaving your current position, the least-harmful choice seems to be to mention that his lab will close and that you chose to study with him in the hope of staying within his wonderful group.

The choice comes down to the problems of being honest (which does not imply you should be dishonest). If you are honest, then because he will retire even if you magically changed his world-view, then the impact would still be negligible. However, you may burn bridges and although a small probability, the professor may take retributive action.

I know it sounds not very ethical, but I said nothing to my supervisor until I'm officially accepted by the new university.

That is almost certainly the best move. Don't say anything to anyone until you've officially been accepted by the other university. Keep working as normal until your acceptance letter comes.

Once you've been accepted to the 2nd university, tell him in person. Stick to a few sentences, and don't mention that your relationship has soured.

Some neutral reasons are

1) If you don't have a stipend here, and school B offers you one, then just cite that reason.

2) You're concerned he will retire before you graduate, meaning you'll have to find another advisor.

He will likely react badly, in general supervisors have limited slots for PhD students dictated by university acceptance. He'll have to wait for the next round of admissions to fill your slot. This is his problem, not yours.

The other answers give the most 'sensible' choice, but being nice and making false excuses for your departure is not the only option.

Consider politely but firmly telling the supervisor your genuine reasons for leaving. There is a risk of backlash (although your supervisor is retiring soon and you are leaving the department) but the upside is the self-respect you will gain from being honest. And if the supervisor is as proud as you say, then they will be just as angry if you say you are leaving to be 'nearer your family' or another excuse.

Too many PhD students are afraid to stand up for themselves because they fear reprisals, but often the opposite is true. If you let more senior academics walk all over you then they will never respect you. If you challenge them then they may be angry in the short-term, but eventually, you will reshape the dynamic and they will treat you more as a peer than an underling. This is essential if you want a long-term career in academia. Always trying to please your superiors may get you through a PhD, but it will not prepare you for leadership.