Group by and Having Clause that uses multiple columns

Question

The AND condition in the below Having clause behaves like it filters the row even if one of the conditions is met when its supposed to be logical AND behavior.

with cte as 
( select 'A' as name , 10 as Classes , 11 as Fees union all
 select 'A' as name , 10 as Classes , 10 as Fees union all
  select 'A' as name , 10 as Classes , 10 as Fees union all
   select 'A' as name , 10 as Classes , 10 as Fees union all
    select 'A' as name , 10 as Classes , 10 as Fees union all
     select 'B' as name , 0 as Classes , 10 as Fees union all
      select 'B' as name , 0 as Classes , 10 as Fees union all
       select 'B' as name , 1 as Classes , 10 as Fees union all
        select 'B' as name , -10 as Classes , 10 as Fees union all
         select 'B' as name , 10 as Classes , 11 as Fees 
       )
       -- A has 50 rooms and 51 $ -- so it should not be returned
       -- B has 1 room and 51 $ and should be fetched
        -- why would the AND in the having clause  behave like a row level filter on only the indivigual column 
        -- instead of the combination
        -- The weird thing is the logic behaves as expected when using = but fails when using <>
       select name , sum(Classes) , sUM(Fees)
       from cte 
       group by name 
       having ( SUM(Classes) !=50) AND (sum(Fees) !=51  )

Here is the weird part if you replace the != with an = like shown below then it works fine

with cte as 
( select 'A' as name , 10 as Classes , 11 as Fees union all
 select 'A' as name , 10 as Classes , 10 as Fees union all
  select 'A' as name , 10 as Classes , 10 as Fees union all
   select 'A' as name , 10 as Classes , 10 as Fees union all
    select 'A' as name , 10 as Classes , 10 as Fees union all
     select 'B' as name , 0 as Classes , 10 as Fees union all
      select 'B' as name , 0 as Classes , 10 as Fees union all
       select 'B' as name , 1 as Classes , 10 as Fees union all
        select 'B' as name , -10 as Classes , 10 as Fees union all
         select 'B' as name , 10 as Classes , 11 as Fees 
       )
       -- A has 50 rooms and 51 $ -- so it should not be returned
       -- B has 1 room and 51 $ and should be fetched
        -- why would the AND in the having clause  behave like a row level filter on only the indivigual column 
        -- instead of the combination
        -- The weird thing is the logic behaves as expected when using = but fails when using <>
       select name , sum(Classes) , sUM(Fees)
       from cte 
       group by name 
       having ( SUM(Classes) =1) AND (sum(Fees) =51  )

Am I missing something when it comes to the way Group by works? I know I can get around the issue but I don't understand why it behaves this way.

This is what I get

This is what I am supposed to get

Answer 1

after some discuss, try use this

 having not(SUM(Classes) =50 AND sum(Fees) =51)

and OP you gotta think twice when you writing boolean.