Exothermicty favours spontanity but does not assure it? please explain it

Spontaneity depends on $\Delta G$. If $\Delta G$ is negative then the reaction is spontaneous. In turn $\Delta G$ is dependent on two factors with the following equation, $\Delta G = \Delta H - T\Delta S$
For the exothermic reaction , $\Delta H$ is negative.
If $\Delta S$ is positive , then the overall  $\Delta G$ becomes negative and hence reaction becomes spontaneous.
If  $\Delta S$ is negative ,then the overall $\Delta G$ becomes positive and hence the reaction is non-spontaneous.
From the above, it can be seen that even though the reaction is exothermic , but it does not assure the spontaneity of the reaction.