Contradiction with John 8:32
Jesus emphasizes knowing the truth and being set free by it, rather than being offended or upset by his words.
John 8:32: And ye shall know the truth, and the truth shall make you free.
Contradiction with Proverbs 11:12
This speaks to understanding and avoiding despising others, which contrasts with taking offense as in John 6:61.
Proverbs 11:12: He that is void of wisdom despiseth his neighbour: but a man of understanding holdeth his peace. [void...: Heb. destitute of heart]
Contradiction with Matthew 11:6
This verse states blessed is he who is not offended in Jesus, which contradicts those who were offended by Jesus' words in John 6:61.
Matthew 11:6: And blessed is [he], whosoever shall not be offended in me.