Arduino UNO code ignores variables selectively
Its hard to see you code, but I think I can make a pretty good guess from your description what is going on.

It seems that you are using the time it takes to increment a value as a way to slow down your code. I think you are underestimating the speed of the arduino. The time it takes to count to 200 (if I'm reading your pictures right) is almost instant; However, you then start printing to with serial each time. Once the serial buffer is full, Serial.print() will wait until there is room in the buffer to place the new value. This time is still small, but making the code wait for it to pass 200 times will take much longer than just waiting for a number to increment to 200.

I think that having added a print statement is slowing down the code enough that your increment based delay is having a noticable effect. What you should do is use the void delay(unsigned long milliseconds); function to cause the code to stop for a bit after it first detects the button has been pressed, and then see if its still pressed afterward. You can also use delayMicroseconds(unsigned int) for shorter but more precise timing. Or better yet, use the unsigned long millis(); function to grab and store the time when the button was activated, and continue polling the current time until the desired delay has been acheived. That way is more code, It allows the code to do something productive while it waits or keep looping.