Don't turn this inward on yourself. I saw this crap with my former clients often, who required access to social security. It being implied you are somehow lesser because you have needs. But here is the thing, this is part of societies contract to people who are unwell. If you have a social security system you have likely jumped through the flaming hoops and soulless bean counters to be recognised as ill and requiring support. Does your father know better? Got relevant credentials to overrule those who stamped this decision into being? I doubt it.
Attaching shame to this money is a standard tactic disincentivise people from taking it. Even though oftentimes it is their money. It then bleeds into the common narrative. Not helped by headlines about lazy people. The usual scrounger rhetoric creating a distorted picture despite fraud figures being very low. Not okay to bail out sick people, but okay to bail out banks and businesses. That is all social security as well... Don't measure your self worth by this. There is plenty that people do in life that has value that cannot be measured via economics alone. If you measure by society's standards you will always fall short. You cannot appease a psychopath that puts productivity before health and even takes from your corpse.
You have to fight from internalising this. When your father is mocking you for claiming disability. I would simply turn it around into a question. What should be done with the disabled then? Do you think they should starve on the street? Be gassed in a truck? The true ugliness on the other side of this line of thinking is already a dark chapter in history. You are not your bank balance and everyone deserve dignity.
If people want to take ownership of tax. Then let them, because it is my taxes also that support you, and I am glad of it. That's what its for and also everyone else's taxes who believe you have the right to dignity and comfort despite illness. Keep that in mind when you are belittled. Keep in mind that everything you spend from that benefit goes back into circulation. That this money is a contract made between citizen and government. One you cannot opt out of. There is no shame in it, beyond the way others wield that shame and how much power you let it have. It must sting to hear this crap from your father but they don't sound like they have any understanding.
I used to have elderly clients, so full of pride that they would prefer to shiver in their flat and live off baked beans then take the money. But I would then point out that they have been paying into insurance for years, now you are simply claiming the government's end of the contract. I had some success reframing it that way because one of the biggest cons is implying that this is not your money, to begin with and you don't deserve it. It's not a character flaw to be ill nor a choice. If you are not claiming fraudulently there should be no shame. In an ideal world, there wouldn't be.
Lastly, your father frankly sounds like a brainwashed muppet to me. But some time in their own future they may need a helping hand too. There will be people out there who won't begrudge them using the safety net as intended either. Because again despite what they said it is what it is for.
Peace