Why does price drop as a result of increase in supply
You are describing a special (although very important) market where the short-run market supply function is vertical : farmers will attempt to sell whatever they have produced, irrespective of what that will do to the unit price. I am not saying this is not reasonable: many agricultural products are not really storable (or require special infrastructure in order to be stored), and there is certainly increased pressure to sell, compared to other products.

And indeed, in such a case, one can see a "good crop" bringing in lower total revenues, due to relatively inelastic demand. This is after all the core reason why government price subsidies in the agricultural sector (i.e. supplementing the farmer's income to compensate for low market price) is the rule rather than the exception, in virtually all market economies around the world, where very few other final products enjoy price subsidies (and only temporarily, while for the agricultural sector, it is essentially a permanent situation, of course not for all agricultural products). 

Also, as another real-world remark,  it is not uncommon for farmers to withhold and even destroy part of their crop in order to safeguard prices (and thus end up with higher total revenues compared to what they would have get if they have sold all the crop at a lower price).

I am not sure I understand the last sentence/question in your post. In what sense farmers "can" or "cannot", "sell at the same or higher price"? And "same" compared to what?