God did intend it for us to have dominion over all animals since the time of creation of this world [Genesis 1:28]. But he expected peaceful coexistence from our side. This could be seen in the Bible. Here, God asks to behave with an Ox working for the Israelites [Deuteronomy 25:4].

This was true with a number of Saints: St Martin Porres, when the rats infested his garden, prayed to God and asked them to dwell somewhere else. He promised to bring them the food there and kept his word too; they relocated to another place in the garden. He was very gentle with them.
God asks us to be thus too. Killing animals and insects for fun by people of any age group is wrong too. It is against his design for the creation.
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