Why is synapse transmission slower than nerve transmission?

Because in the nerves it is a electrical signal (quick) that has to be converted to a chemical signal (slower) at the synapse.
##color(blue)The electrical signal##
The signal that travels through nerves to a target (axons) is called an action potential. This is an electrical signal because it is mediated by charged molecules (ions).
Receptors in the axons are sensitive to changes in this charge which propagates the signal. This is a very quick process.
##color(blue)The chemical signal##
Between nerve cells there is a gap called the synapse. Since the electrical signal can’t simply cross that gap it has to be converted to a chemical signal.
So at the synapse the electrical signal causes a series of reactions. This leads to the release of vesicles containing messenger molecules (neurotransmitters). These neurotransmitters have to cross the gap by diffusion which is relatively slow .
At the other side of the gap the neurotransmitters have to bind to a specific receptor. This receptor converts the chemical signal back into an electrical signal.