give me an example that fits this statement.

[YAX]

A is B and B should be A, but A does not equal B.

Here's what I can think of:

 
 

[YAX]

uhhh.. okaaay.  another?

[kyrie_eleison]

Let's see,

Me + your wife = a kid
You + your wife = mother + surrogate father
You vs. Me = You being owned...

hahahaha.  I love this website. 

[YAX]

yah.. you da funnay.  I have no idea what your example is saying, but you da funnay.

Okay. Next.

[kyrie_eleison]

yah.. you da funnay.  I have no idea what your example is saying, but you da funnay.

Okay. Next.

Are you asking what's next?  You're owned...what else is there?

[YAX]

 

[Peachy Fish]

LOL. Tried my best and all I could think of this moment is the following:

Sun is star and Star is sun, but Sun does not equal all stars

[Reporter]

The whole is greater than the sum of its parts, although the parts are taken from the whole itself.

[YAX]

LOL. Tried my best and all I could think of this moment is the following:

Sun is star and Star is sun, but Sun does not equal all stars

hmm. not bad.

[trepidpoda]

A is B and B should be A, but A does not equal B.

Here's what I can think of:
 

A is a circle.  B is also another circle.  A part of both circles A and B are superimposed, where as the rest is not.

[Mr. Complicated]

A is B and B should be A, but A does not equal B.

Here's what I can think of:

 

Time is space, and space should be time, but time does not equal space.

Dreaming is thinking, and thinking should be dreaming, but dreaming does not equal thinking.

A real number is a rational number, and a rational number should be a real number, but real numbers does not equal rational numbers.

Sex is love, and love should be sex, but sex does not equal love.

[8v10un30sun]

A is B and B should be A, but A does not equal B.

Here's what I can think of:
 

This is play on word.  You said should versus shall vs is.  Should is MAYBE, MIGHT, etc...  So B might be A, hence the logic fails to prove equivalence.  Unless otherwise defined, should is not equal to shall.

You should be home at 5pm indicates that you might be home at 5pm.  Hit or miss...no certainty.

You shall be home at 5pm indicates a command, a requirement, hence it's a certainty.