How can I get my deposit back from the landlord?

The landlord must give you an itemized list of damages with costs or return your deposit within 30 days. Check out the Michigan Landlord Tenant Handbook its available for free to download from Michigan.gov

He has to send you within 21 days of your vacating a list of what he is deducting and for what reason. Send him a letter pointing that out and giving him 5 days to refund your money or you will go to small Claims Court. If the painting is needed just because of the normal wear from your having lived there [or because a new tenant demanded it be repainted] you would not be responsible even if the landlord sent you the list within 21 days.

I need details, but it is clear he is making some claim for damages.

You can sue for triple damages.

The Washington Landlord Tenant Act requires a landlord to refund a deposit or provide an accounting for it within 14-days from the date you move out. If you have not gotten this from the landlord, you can sue for the full deposit back plus your fees and costs incurred. Most often, however, tenants bring small claims suit against their landlord. You should take the bills from the landlord and consult with an attorney representing tenants so that you can address the landlord's claims as well as the deposit issue. Even if you win your deposit back, you might still be liable for any legitimate damages beyond reasonable wear and tear.