My first ex tried to break up with me countless times over petty reasons or because she didn't think she was "good enough". Now that I think about it she didn't actually want to break up but wanted to be reassured and be talked out of it, it was an immature game and I made the mistake of entertaining her each and every time. I eventually left her because she cheated.
My most recent ex has also done this 3 times, the third was the last and final one. She eventually decided she couldn't neither accept how I am nor wait for me to do things on my own pace.
Now I decided I'm absolutely done with this bullshit, you can either stay or go but don't fuck around. If you have doubts we can talk or you can take a break to think things through but I will personally stop tolerating this immature and inconsiderate bullshit.
To each their own but since you're barely at the start of your relationship it's highly likely this will reoccur. I find it highly disrespectful to play with someone's feelings and sense of security like this. It's up to you if you feel like this is something you can put up with undefinitively or until one of you decides to break up for good.