You're not being blackmailed; as a general matter, insurers may put conditions on providing coverage, and if you don't like their conditions, you can look for other coverage. In point of fact, it is probably perfectly reasonable to require that a house be painted, if the paint is older or peeling (or if the home is unpainted at present)--paint helps protect the surface underneath from the elements, such as from rain or moisture-caused rot. (That's why bridges are painted, for example--not for looks but to protect them from corrosion.)
It's not impossible your insurer does not want your business and is looking for a way to encourage you to go elsewhere for coverage; however, other than that, there is no benefit to the insurer from you painting your house--it's not like you're hiring them to do this. They are very likely requring it to help protect the physical structure of your home, which does reduce the likelihood of a claim. You certainly could ask them "why" they are requring it, but I strongly suspect it's for the reason stated.
As J.M.A. stated, if there is a policy currently in force, you can check the terms of the policy and if there is no authority or grounds in the policy for them to require this or cancel, they cannot--while the policy is in force, the insurer is bound by its terms. However, they may make new terms or requirements for renewal.
If this is mid-term, or while a policy is in force, you should also ask your insurer to point to the terms or conditions in the policy that they believe gives them to right to require painting.
And, of course, you can contact other insurers to see if they will cover your home, and for how much.