Revelation 13:3
"And I saw one of his heads as it were wounded to death; and his deadly wound was healed: and all the world wondered after the beast."
Where did you get the doctrine that Satan cannot heal? If sickness came from the devil, you mean he cannot remove it, in order to accomplish his purpose?
You're misapplying a parable and out of context...
Context shows better what this so called "healing" is.
It's pretense of being healed when one is actually not healed at all:
Jeremiah 6:14 They have healed also the hurt
of the daughter of my people slightly,
saying, Peace, peace; when there is no peace.
Was there an actual healing? Can satan provide peace? Can satan heal their wound?
But why not pull more context on the very example you gave. The context says that the beast "was, and
is not".
"Is not", means the beast is actually DEAD. Which is why it's such a marvel about it still going.
Our old unregenerate wild man (=the beast) was crucified at the cross, Jesus gave it a deadly wound. It's a defeated foe.
We see the same thing with the first Adam, our old man (the new man being Christ). Death moved into Adam's body because he ate of the tree, deadly wound was given to the flesh
in that day that he ate of the tree, right away death was written into the body, just like God said it would. Adam is actually dead as per God's promise. Yet, Adam doesn't seem to be dying immediately ("and yet is"). It is the same with all of us. Death is coded into our physical bodies because of sin. People are dead in their sins. But satan runs his "self help" campaign saying peace, peace, as if we can have life in the body of sin. There is no life in it. Satan can heal no one.
Where did i get the doctrine that satan cannot heal or cast demons out?
Here: I paraphrased Jesus in my original post,
Matthew 12:22 Then was brought unto him one possessed with a devil, blind, and dumb: and he healed him, insomuch that the blind and dumb both spake and saw. (...)
24 But when the Pharisees heard it, they said, This fellow doth not cast out devils, but by Beelzebub the prince of the devils.
25 And Jesus knew their thoughts, and said unto them, Every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand:
26 And if Satan cast out Satan, he is divided against himself; how shall then his kingdom stand?
27 And if I by Beelzebub cast out devils, by whom do your children cast them out? therefore they shall be your judges.
28 But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.
29 Or else how can one enter into a strong man's house, and spoil his goods, except he first bind the strong man? and then he will spoil his house.
Mark 3:22 And the scribes which came down from Jerusalem said, He hath Beelzebub, and by the prince of the devils casteth he out devils.
23 And he called them unto him, and said unto them in parables, How can Satan cast out Satan?
24 And if a kingdom be divided against itself, that kingdom cannot stand.
25 And if a house be divided against itself, that house cannot stand.
26 And if Satan rise up against himself, and be divided, he cannot stand, but hath an end.
27 No man can enter into a strong man's house, and spoil his goods, except he will first bind the strong man; and then he will spoil his house.
28 Verily I say unto you, All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme:
29 But he that shall blaspheme against the Holy Ghost hath never forgiveness, but is in danger of eternal damnation:
30 Because they said, He hath an unclean spirit.
