I have had Tentacruel, Starmie, Ninetales, Scyther, and a few others run away from me after a few failed attempts at catching them. Yet my wife and son standing right next to me catch them. Is there a glitch in my app? Why is it I am the only one who has these rare pokemon run away? Wartortle was another one.
Pokémon spawn are identical between different players in the area, but the Pokémon statistics are derived from your level.
If you are level 25 and your family is around level 5, your Pokémon will be potentially much higher CP, causing their chance to run away to go up.
In addition, the Pokémon running away is a random event so there also discrepancy between players due to randomness.
To add to what Nelson said, there are other factors that determine qhethwr or not the pokemon will be caught. Starting off, the ball you throw. Such pokemon are usually hard to catch, so the use of pokéballs instead of greatballs or ultraballs could lead to them running away. Also, the way you throw the ball also has an impact on the catch chance. Lastly, there is the chance that your family used razz (or rasp i cant remember ) berries which makes the pokémon easier to catch.
I really doubt i was of help to you but maybe I can help aome other usees as well.