When a creature with summoning sickness is equipped with a haste-giving equipment and the turn is passed to the next player, destroying, sacrificing, or removing the haste giving equipment does not give the creature summoning sickness again as it should. Instead the creature is able to activate it's abilities as though it had haste.

To replicate: play any creature with an activated ability and without haste, equip it with an equipment that gives it haste, pass the turn, destroy or sacrifice that equipment. The creature can now still activate abilities as though it had haste.