Step 1: Understanding the Concept
A spontaneous process takes place on its own under given conditions, without continuous outside help.
Step 2: Check each statement
A: true, it occurs of its own.
C: true, spontaneity is a thermodynamic idea and says nothing about the rate.
D: true, it continues until equilibrium is reached.
Step 3: The false statement
B says the process runs in both directions without any external agency. A spontaneous process is one-way; its reverse needs external work.
Final Answer:
The statement that a spontaneous process proceeds in both directions without an external agency is not true.
\[ \boxed{\text{(B) }\text{It proceeds in both directions even in absence of external stimulant.}} \]