7 When a Samaritan woman came to draw water, Jesus said to her, “Will you give me a drink?” 8 (His disciples had gone into the town to buy food.)
9 The Samaritan woman said to him, “You are a Jew and I am a Samaritan woman. How can you ask me for a drink?” (For Jews do not associate with Samaritans.[a]) (John 4:7-9 NIV)
This passage shows that Jesus was not afraid to violate cultural taboos in order to give the gospel to others. The woman at the well was shocked that He would talk to her. Most Jews would never have asked a Samaritan, let alone a woman for a drink no matter how thirsty they were!
But Jesus was eager to talk to her because he cared about her and wanted her to repented about her sins. I don’t think that he really cares that much about getting a drink of water; He is simply trying to start a conversation with her so that He can reveal to her the truth of the gospel.