Many critics have the habit of quoting scriptures out of context to make a point that Jesus wasn’t God. However, looking at the immediate context makes it a lot easier for us to understand why Jesus was not able to do any miracles as reported in the book of Mark. Let us read verses 5-6 to get to the depth of this issue:
Mark 6:5-6 New International Version (NIV)
5 He could not do any miracles there, except lay his hands on a few sick people and heal them. 6 He was amazed at their lack of faith.
Notice that Jesus did perform miracles as we read in the latter half of verse 5. But in verse 6 we read that he was amazed at their lack of faith. Thus Jesus, even though physically being able to perform miracles, volitionally put up a restriction on doing any miracle because of their lack of faith. Jesus was able to do it but He wasn’t willing to do it because they rejected him. Also, Matthew 13:58 makes it crystal clear:
Matthew 13:58 New International Version (NIV)
58 And he did not do many miracles there because of their lack of faith.
If we go back to verse 3 we read that they were offended by Jesus because according to them he was just an ordinary carpenter and still he was teaching and performing miracles as if He had some sort of authority. So as we see, even his act of healing was offensive to them and it led to his unwillingness of continuing the healing ministry.