The teacher is always wrong, flip his answer

05AB1E, 45 41 40 39 38 bytes

Code:

“‰¦žä¥æ€¸pe…Ü€¸“ð¡2ôDí«D€™«vy`:D_D¹Êiq

Explanation:

It first starts with the compression:

“‰¦žä¥æ€¸pe…Ü€¸“

This is a compressed version of "true false yeah nope yes no". After that, we split on the spaces with ð¡, resulting into:

['true', 'false', 'yeah', 'nope', 'yes', 'no']

We slice this array into pieces of 2 with 2ô, resulting into:

[['true', 'false'], ['yeah', 'nope'], ['yes', 'no']]

We duplicate this array and reverse each element of it with Dí. Then we append this to our first array with «, resulting into:

[['true', 'false'], ['yeah', 'nope'], ['yes', 'no'], ['false', 'true'], ['nope', 'yeah'], ['no', 'yes']]

To get the titlecased words, we duplicate the array again and convert each word to titlecase with €™. Finally, this is appended to the initial array. So, the final list is:

[['true', 'false'],
 ['yeah', 'nope'],
 ['yes', 'no'],
 ['false', 'true'],
 ['nope', 'yeah'],
 ['no', 'yes'],
 ['True', 'False'],
 ['Yeah', 'Nope'],
 ['Yes', 'No'],
 ['False', 'True'],
 ['Nope', 'Yeah'],
 ['No', 'Yes']]

The imporant part here is that Nope comes before No. Eventually, we get to this part of the code:

vy`:D_D¹Êiq

Explanation:

v            # For each in the array...
 y`          #   Push the array (containing 2 words) and flatten.
   :         #   Replace the first word with the second.
    D_       #   Duplicate and negate (resulting 0 into 1 and 1 into 0).
                 If this is not possible, this results into nothing.
      D      #   Duplicate the top of the stack again.
       ¹Ê    #   If it's not equal to the inital input string...
         iq  #     Quit the program and implicitly print the processed string.

Uses the CP-1252 encoding. Try it online!.

Pyth, 44 bytes

j\.XXXcz\.`M2)Jc."<unprintables>"\b)rR3J

Hexdump:

00: 6A5C 2E58 5858 637A 5C2E 604D 3229 4A63
10: 2E22 6179 0862 3C40 D23B 9A54 C2B4 A20A
20: FEE7 8701 225C 6229 7252 334A

Test suite.

TI-Basic, 217 bytes

Longer than I thought it would be...

Input Str1
If Str1="0
Then
Disp 1
Stop
End
"e"=sub(Str1,2,1
sub("FalsefalseNopenope",1+5not(Ans)(sub(Str1,1,1)="t")+10Ans+4Ans(sub(Str1,1,1)="y"),5-Ans-2(sub(Str1,3,1)="s"))+sub(" .",1+(sub(Str1,length(Str1),1)="."),1