why DO a CYCLE cannot STAND without a support its STAND?

Dear Adit, 

A bicycle or any other two-wheeler cannot stand because even if both wheels are on the ground and the system is in equilibrium, the equilibrium is always unstable. When a stand is added, there are 3 supports and stable equilibrium is possible.

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Askiitians Expert

Chetan Mandayam Nayakar – IIT Madras  

It is due to the unstable equillibrium  without stand.
When the cycle is on stand then the vertical component of weight of the cycle(i.e., mg*sinthita) acts exactly opposite to the normal reaction hence balancing the cycle. It does not matter how many supports you have on cycle only one support is sufficient but it must be able to make cycle reach equillibrium.