What does Matthew 16:3 mean?

Some Pharisees and Sadducees had approached Jesus together to ask Him for a "sign from heaven." They want Him to perform some miraculous work to back up claims He was the Messiah. Since these two groups of religious leaders often opposed each other, it is a sign of their urgent concern about Jesus that they are cooperating to discredit Him.

Jesus has pointed out that some signs require nothing more than common sense to interpret. Basic weather is an example. These skeptics who claim they have not seen enough from Jesus can notice weather patterns in the sky to determine whether it will be fair or stormy. Jesus' words in verses two and three echo a common expression in English: "red sky in the morning, sailor take warning; red sky at night, sailor's delight." Typical patterns in nature lead to obvious general conclusions.

Despite their ability to recognize these weather patterns, the religious leaders have apparently not chosen to recognize the "signs of the times." They have witnessed Jesus' miraculous healings and casting out of demons (Matthew 12:13–14, 22). They have read the words of Isaiah (Isaiah 35:5–6; 61:1–2) and seen them come to life before their eyes. As Jesus described His work to John the Baptist, "the blind receive their sight and the lame walk, lepers are cleansed and the deaf hear, and the dead are raised up, and the poor have good news preached to them" (Matthew 11:5).

These men are not suffering from a lack of evidence. They are suffering from stubbornness. Their refusal (John 5:39–40) to recognize Jesus as Messiah is insincere, and it's why Jesus refuses to satisfy their request. He's not going to perform for them, on a whim, and when it won't matter, anyway.