Matthew 15:
1 Then Pharisees and scribes came to Jesus from Jerusalem and said, 2“Why do your disciples break the tradition of the elders? For they do not wash their hands when they eat.”
Why would Jesus speak against washing hands?
He didn't. Mark gave more details in Chapter 7:
1 Now when the Pharisees gathered to him, with some of the scribes who had come from Jerusalem, 2they saw that some of his disciples ate with hands that were defiled, that is, unwashed
i.e., so-called unwashed.
The Greek word here rendered "defiled", literally signifies "common". The Pharisees prescribed a hand-washing procedure. New Living Translation is helpful for Mark 7:
2 They noticed that some of his disciples failed to follow the Jewish ritual of hand washing before eating.
Jesus and his disciples did not ceremonially follow that system.
3 (For the Pharisees and all the Jews do not eat unless they wash their hands properly
ESV footnote: Greek: unless they wash their hands with a fist, probably indicating a kind of ceremonial washing
holding to the tradition of the elders,
i.e., the traditional procedure
4and when they come from the marketplace, they do not eat unless they wash.
Greek: unless they
baptize; some manuscripts unless they purify themselves
And there are many other traditions that they observe, such as the washing of cups and pots and copper vessels and dining couches.)
They were overdoing the washing ceremonies.
5 And the Pharisees and the scribes asked him, “Why do your disciples not walk according to the tradition of the elders, but eat with defiled hands?”
Then Jesus explained to them that they did not eat with defiled hands.
Pulpit thought that they did wash their hands but not according to the procedure prescribed by the Pharisees:
St. Mark explains the meaning of the word κοιναῖς (literally, common), by the word (ἀνίπτοις) "unwashen." The disciples, doubtless, washed their hands, but they abstained from the multiplied ceremonial washings of the Pharisees, which they had received by tradition and punctiliously observed. The scribes and Pharisees, who had come from Jerusalem, were doubtless sent as spies, to watch and to report in no friendly spirit the proceedings of the great Prophet of Nazareth.
The Pharisees were watching and nitpicking.
Back to Matthew 15:
1 Then Pharisees and scribes came to Jesus from Jerusalem and said, 2“Why do your disciples break the tradition of the elders? For they do not wash their hands when they eat.” 3He answered them, “And why do you break the commandment of God for the sake of your tradition? 4 For God commanded, ‘Honor your father and your mother,’ and, ‘Whoever reviles father or mother must surely die.’ 5 But you say, ‘If anyone tells his father or his mother, “What you would have gained from me is given to God,” 6he need not honor his father.’ So for the sake of your tradition you have made void the wordb of God. 7You hypocrites! Well did Isaiah prophesy of you, when he said:
8“‘This people honors me with their lips, but their heart is far from me; 9in vain do they worship me, teaching as doctrines the commandments of men.’”
Jesus wasn't against washing hands; he was against the practice of washing hands ritualistically as a doctrine of worshiping God. You can wash your hands any time you want, but it is not a form of worship.
Surely he knew that this was of great health benefit. He might have had an issue with the ritual but why do you think he would speak against a practice that would save many lives?
Jesus did not recommend anyone to eat with filthy hands, and Jesus ate with his hands without using any fork.
