My child told me they are gay/lesbian
Before You Begin
Pause and breathe. Even if this shouldn't be happening... accept that it is and embrace it with composure and calmness.
Calmness is the only way forward because without calm, there is no possibility for receptiveness and connection. Your child won't give to you any more than they see from you.
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Never forget that a strong connection is fundamental, as there will be no correction in them if there is no connection with you.
The Core Problem
Depending on your beliefs, this may or may not be a problem but it is certainly an important time in their life that needs to be handled well.
This is a rare circumstance where "a win" is more defined by the parent's ability to have unwavering empathy, connection with, and love for their child throughout the conversations on this topic.
What Will Make It Worse
Ignoring your child's attempts to discuss this side of themselves or having a negative response won't change how they feel, it will only deteriorate your relationship with them and make their journey more troubling.
What The Child Needs
1. To further understand where they are at: Your child likely has a lot to think through, and while much of it should be private to them, having them explain to you what they are feeling and why they came to this conclusion is important for both of you.
2. To keep things from snowballing: Unfortunately, it's not uncommon for parents to push their child away after hearing this news. This could lead to compounding negative effects. For example, kicking the child out of the house could lead to them not finishing high school or college, which will then hurt their ability to get a good job, and so on. While you are not required to be happy about it, don't damage the rest of their life in how you handle this.
3. To always feel the love of their parents: They are still your child, and the same person they were before they brought this up to you. If you're unable to provide your full support, assure them that your love is unconditional, and support may simply be more overt in other areas. Your child will appreciate knowing in their heart that you will never turn your back on them, and that you are doing your best.
4. To meet others like them: Your child meeting relatable peers of a similar age, upbringing, religion, etc. that they can talk to about being gay to further their understanding of themselves, and this new world, could be very beneficial to them. Or it could make them realize that they aren't like that person, and don't feel comfortable in that community. Either way, the experience will give your child more confidence in understanding their sexuality.
How To Have The Conversation With Your Child
Find a time where you and the child are relaxed and can talk in an environment that is private, comfortable and distraction free.
Let them know that you are open to hearing what they think about being gay and all the emotions they are feeling. Share that you are guessing this is one of the most difficult times in their life, and you don't want them to feel alone.
Have a two-way conversation with mutual respect, that encourages full, unguarded honesty, even if you and your child aren't in the same place of accepting this change.
While points 2-4 of "What The Child Needs" are critical to a positive outcome, they aren't necessarily provided as talking points for this conversation. If you do touch on them in your conversation, it wouldn't be a bad thing as they would indicate to your child that, regardless of how you are feeling, maintaining a strong relationship with them is very important to you.
Throughout this first and later conversations, keeping a mental distinction between your child and their sexuality will allow you to be at your best in your reactions and in simply being there for them, even if you don't know how you feel or flat out don't support it.