I recently took a vacation that involved flying across the ocean. Since it was a long overnight flight, passengers were provided with little "kits" including a toothbrush and a tiny tube of toothpaste, slippers and so on.
I tried to get some sleep on the flight, and when I awoke, I went to the lavatory to freshen up. When I unscrewed the cap from the tiny tube of toothpaste, I discovered the tube was sealed. Since I didn't have anything with me to pierce the seal, I tried to pop out the seal by squeezing the tube. This resulted in the side of the tube splitting open and sending toothpaste all over my trousers!
When I got back to my seat, I told my wife about my experience. She showed me how the seal could be broken by using the small piercing tool in the top of the toothpaste cap. (See arrow.) Many people might blame themselves for not knowing how to open the toothpaste tube, but I opt to blame the designers of this tube for not making it more obvious how to open it. After all, I am no different than many people who have never seen a tiny toothpaste tube that opens in this way. And perhaps they, like me, will have to figure out how to open the tube while still half asleep.
Design suggestion
A more obvious design might be to provide the type of sealed cap used on many soft-drink bottles, where unscrewing the cap breaks the seal.
At the very least it would be helpful to include directions on the tube for piercing the seal. The directions should be illustrated graphically so they could be understood by speakers of any language.