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[Denni]

I do not do TKinter but if I had to venture a guess it is one of two things or both:

You open the file with open("animals.txt", "w") aka overwrite mode (I believe) try open("animals.txt", "a") or append mode

The .write() might overwrite as such what you need would be .append()

Note you will have to check the syntax of those two suggestions as again I do not do TKinter but it ought to have something like that.