Jesus stretched out His hand toward his disciples and said,
“Here are my mother and my brothers"
MATTHEW 12 : 48
Stretch means to extend or expand, reach out, draw up, cause to reach or continue. (Merriam-Webster). In this reading, Jesus extends His hand to emphasize that all who are with Him is His family.
"Stretch out His hand" is a phrase that can be used in different contexts. It can mean to reach something out to someone or something1. In a biblical context, it can refer to a story in which Jesus heals a man with a withered hand. Jesus tells the man to "Stretch out your hand," and the man's hand is restored. (Idioms - Free Dictionary)
At the start of story of Job, there is a recurring phrase - ‘stretch out your hand and touch’ (Job 1:11, 2:5). The accuser is demanding this of the Lord. What is the meaning of the two parts (stretch out your hand [and] touch.) in this Hebraic phrase? This seems to be a Hebraic idiom. Here, the accuser is asking the Lord to do something. But, what?
The expression which is translated "can't afford" or "too poor" is literally "your hand can't reach". When your hand can't reach something, or something is outside your grasp, then it is impossible for you to accomplish. But God is omnipotent, and His hand can reach everywhere, and this is often used when visiting destruction: "And the Egyptians will know that I am Yahweh when I stretch out my hand over Egypt and bring the Israelites out from their midst (Ex 7.5). And I will stretch out my hand against them, and I will make the land a desolation and a wasteland from the desert to Riblah in all of their dwellings, and they will know that I am Yahweh (Eze 6.14). And their houses will be turned over to others, their fields and their wives together. For I will stretch out my hand against the inhabitants of the land,” declares Yahweh (Jer 6.12).
It's really important to understand that when you are talking about word pictures and imagery, it is a great error to assume that each word picture is limited to a single root or lemma. When there is a metaphor that something in the reach of your hand is within your power, then it does not matter if you are reaching, grabbing, stretching, swooping, with your hand. All of these are examples of this hand-reaching metaphor. (Biblical Hermeneutics)