Chemically speaking, why dose alcohol make people feel drunk and cannabis make people feel high?

its all about receptors, a chemical such as or similar to THC in cannabis is made naturally in our body but is short lived and in low amounts, we feel high because it stimulates all the receptors in our brain or body.

alcohol is the same concept, look to wikipedia for the exact receptors

Cannabis stimulates a group of receptors called cannabinoid receptors on neurons in different parts of the central nervous system (responsible for the different effects!!), i.e., the neurons in the limbic system affect emotions, the hippocampus and amygdala cause memory problems, cerebellar neuron effects cause coordination problems, etc.

Alcohol functions very similarly, affecting different neurons and receptors.  Alcohol stimulates a type of receptor called a GABA-A receptor, which is a way that brain cell function is depressed.  Basically this is why people's inhibitions are lowered, they lose the pathway that would "regulate their actions" as per social codes (violence, sexual misconduct, etc.).  This pathway also depresses function in the cerebellum, causing loss of muscle coordination and problems walking (ataxia), and the depression in the reticular formation neurons lead to decrease in consciousness "passing out".

Another type of receptor involved is a type of glutamate receptor (which is stimulatory), which is INHIBITED by alcohol.  So normal pathways here are blocked or depressed.  This receptor is called an NMDA receptor, and this blocking effect causes memory loss ("blackouts"), tremor (called delerium tremens in severe alcoholics), and withdrawal, along with other severe psychological effects.