It is pretty well impossible to "pull" out a dandelion, unless it is very immature and is in soft wet soil.
Dandelions have very long tap roots that almost require backhoes to get them out, especially if they have taken root in soils that have a lot of clay. Many plants require good rich soil to grow in, not dandelions, they can grow pretty well anywhere.
Try some long, skinny tool, such as mentioned above. You need something to get down deep, hopefully below the root, so you don't snap that root. But also try to have your soil in a soft state, by that I mean moist.
If you do not get out all of the tap root, or if you snap or cut it in two, the dandelion will come back and when it does, it will come back bigger and fatter
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