Is it unusual to love one movement of a work and dislike the others?

I'm not sure about "unusual" but I can think of several works that have one very popular movement that's often played, but the complete work is seldom heard, indicating that the classical-loving public feels much as you do.

For examples:

the 2nd movement (Scherzo) from Litolff's Concerto Symphonique #4

the 5th movement (Toccata) from Widor's 5th Organ Symphony

the 4th movement (Adagietto) from Mahler's 5th Symphony

the 2nd movement of Barber's String Quartet, op. 11 (usually in the arrangement for full string orchestra)

(and I'm sure there are more, the names of which escape me just now)

Usually, the first and last movements are for technique, while the middle one is for lyricism. If you like the way the composer uses their techniques, you may like that movement more. If you like the way music flows, you might like the 2nd movement more. It all depends. 

Of course it is normal for us human beings to like certain movements and dislike other works or pieces. Ling Ling however, listens to all pieces of classical music at once

No, it's not.  I like Beethoven's Moonlight Sonata, 1st and 3rd Movements but not the 2nd.

I love the slow movement from Beethoven's 7th and the Adagietto from Mahler's 5th, there's nothing wrong with listening that way I think. 

No, it's not unusual. I believe most people who listen classical works have favorite movements including myself. Even though I have favorite movements I still listen to the entire work. To each his/her own.

I don't care if it's unusual or not, I don't like the first movement of some things.

It's okay by me.  I like the Mozart horn concertos, but I'm not fond of the second movements.