When you feel that, you are being avoided by your loved ones and there is no other solution other than being far away from them, in those situations follow the below tip, which might be genuinely suitable to anyone.
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If the person is your loved ones, obviously you might be aware of their mentality. So if such person is avoiding you, definitely there might be some disturbance that you created in them, though not intentionally. In those situations, instead of asking them for the reason, you move away from them.
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Then a day may come, where they would come to you and ask for the reason behind your silence. Then explain that, you did it, so as to make them free. Then the actual issue comes out from the opposite person and thus can be sorted out with the mutual discussion.