Please explain the difference in this example

Hi Claudia,

Jacques lui manque is the correct way, with lui replacing the person who misses Jacque. If the person is mentioned directly, the construction changes: Jacques manque à Anne -- Anne misses Jacques. She misses Jacques -- Jacques lui manque. 

On another note and to confuse matters slightly:

Je pense à toi -- I'm thinking of you. Correct.
Je te pense. -- INCORRECT

Alain me manque   

How can that be wrong?  It doesn't make any sense -

Alain me manque. -- I miss Alain.
Je manque à Alain. -- Alain misses me.