@jatin khachane 1,
Your interpretation has a slight mistake,
q if p.. means p is sufficient condition of q....but q can happen without p
Upto this it is right. Then you said p $\rightarrow$ q is not valid. But why? Since q can happen without p so even if p is False, q can be anything (it may happen or not happen i.e. q can be T or F) and still the outcome should be valid. p $\rightarrow$ q exactly satisfies this condition. When p=F, q can be anything. And when p is T, q has to be T.
Eg: For checking whether a graph is Hamiltonian, Dirac's theorem is sufficient. Means if theorem is satisfied then graph is Hamiltonian but if not satisfied, then graph can be anything. We can't conclude.
p: Graph satisfies Dirac's Theorem.
q: Graph is Hamiltonian
p is sufficient condition of q
p $\rightarrow$ q
So when p is T, q has to be T.