What determines whether the response of a receiving neuron is excitatory or inhibitory?

Whether the response of a receiving neuron is excitatory or inhibitory is determined by the neurotransmitter that the presynaptic neuron releases and the receptors that the receiving neuron expresses.

Excitatory neurotransmitters: When a presynaptic neuron releases an excitatory neurotransmitter, such as glutamate, it binds to receptors on the receiving neuron that allow positively charged ions (such as sodium ions) to flow into the cell. This influx of positive ions depolarizes the neuron, making it more likely to fire an action potential.

Inhibitory neurotransmitters: When a presynaptic neuron releases an inhibitory neurotransmitter, such as GABA or glycine, it binds to receptors on the receiving neuron that allow negatively charged ions (such as chloride ions) to flow into the cell or positively charged ions (such as potassium ions) to flow out of the cell. This efflux of positive ions or influx of negative ions hyperpolarizes the neuron, making it less likely to fire an action potential.

The net effect of the excitatory and inhibitory inputs that a neuron receives determines its firing rate. If the excitatory inputs are stronger than the inhibitory inputs, the neuron will fire an action potential. If the inhibitory inputs are stronger than the excitatory inputs, the neuron will not fire an action potential.