The phrase "shows the gate to" generally means to dismiss, expel, or remove someone from a place or situation. Some antonyms for this phrase could include welcoming, accepting, embracing, allowing, or inviting someone to stay. Instead of showing the gate to someone, one could offer hospitality, extend an invitation, open the door for them, or give them a warm reception. Other antonyms could include supporting, assisting, aiding, or encouraging someone to stay and participate in a given activity or event. Ultimately, the opposite of showing the gate to someone is being inclusive and supportive of their presence and involvement.