Why Does My Python While Loop Print "Wrong answer!" After a Correct Guess?

The while loop (it's not a function!) head is (here) independent from what you do in the loop's body. When the loop condition is true, the whole code in the body runs. If that code prints something unconditionally (i.e., without using an if to check whether it should print), then you get that output. After the body is finished, the loop's condition is evaluated again, and the loop may or may not start over.

Stating it differently: the loop head determines if the body should run again, and that check happens when the body is finished. The whole body runs, unless you use break or continue to exit the loop early.

I'll answer to your second question first: Why does the initial code always print Wrong Answer! regardless of the given answer?

Let's look at the body of the while loop:

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if guess_count < guess_limit:
    guess = input("Enter guess: ")
    guess_count += 1
    print("Wrong answer!")
else:
    out_of_guesses = True

We know that the condition of the if statement evaluates to True, since we just entered our guess (the if body is executed, not the else). The program received our input.

Next, with guess_count += 1, the program increments the guess count. This does not show anything different to the user.

Finally, print("Wrong answer!") makes the program state that the received answer is wrong, without even checking whether it is actually wrong. It is always executed after receiving any input.

If you modify the code by placing break right after the print statement, the control flow will exit the loop. However, the program has already printed that the answer is wrong. Adding a break does not change anything here.

Now, let's move on to the first question: What is the while loop for?

Let's have a look at the condition of the while loop:

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while guess != secret_word and not (out_of_guesses):

If the previous guess matches the secret word, the program stops running the loop. Otherwise, it checks if the user is out of guesses, and if so, it stops running the loop as well.

To prevent the program from printing Wrong answer! unnecessarily, we could add an if statement wrapping it and then rely on the while loop to exit:

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while guess != secret_word and not (out_of_guesses):
    if guess_count < guess_limit:
        guess = input("Enter guess: ")
        guess_count += 1
        if guess != secret_word:
            print("Wrong answer!")
    else:
        out_of_guesses = True

if out_of_guesses:
        print("Out of Guesses, YOU LOSE!")
else:
        print("Correct!")

In some other languages, we might use a do ... while construct to avoid duplicating the if statement. However, since Python does not support do ... while, moving the while condition to the if condition, as suggested in other answers, seems to be the best approach for now.

I modified your code as follows:

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secret_word = "giraffe"
guess = ' '
guess_count = 0
guess_limit = 3
out_of_guesses = False
    
# removed the condition guess != secret_word in while loop

while guess_count < guess_limit:
    guess = input("Enter guess: ")
    
    # conditional if statement for guess != secret_word:
    
    if guess != secret_word: 
        print("Wrong answer!")
    
        #loop continues only on this condition
    
        guess_count += 1 
    
    else:
        print("Correct!")
        break # break loop
    
# if guess_count is equal to guess_limit, 'Out of guesses' printed
    
if guess_count == guess_limit:
    
    print("Out of Guesses, YOU LOSE!")

Let's review your code (the second one):
Let's see the first line after the while (we will see the condition of it later)

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while guess != secret_word and not (out_of_guesses):
    if guess_count < guess_limit:

Let's think about the first iteration, we haven't done anything, and we already ask if it has exceeded the number of attempts, it's true, it doesn't make sense, so we'll leave that line for later.
we then prompt the user to enter a word

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guess = input("Enter guess: ")

then we compare it with the secret word, and if they match... we return True and exit the while, this avoids one of the while conditions.

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if guess == secret_word:
    print("Correct!")
    break
else:
    print("Wrong answer!")

if it has not entered the if and exited the while, now if we increase the number of attempts

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guess_count += 1

if the number of attempts has been exceeded, the appropriate message is printed and the while is exited.

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if guess_limit == guess_count:
    print("Out of Guesses, YOU LOSE!")  
    # the "out_of_guesses" variable becomes meaningless
    break

now we review the conditions of the while, since the comparison of the secret word and the entered one is done in the body of the while, we remove it from the conditions, the same happens with the limit of attempts, so we replace the previous conditions by:

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while( True ): 
    guess = input("Enter guess: ")

    if guess == secret_word:
        print("Correct!")
        break
    else:
        print("Wrong answer!")

    guess_count += 1

    if guess_limit == guess_count:
        print("Out of Guesses, YOU LOSE!")
        break