Reasons for this need can include being a highly sensitive person, an introvert, or leaning towards avoidant attachment. When you're not in conflict, explain to your partner how it feels to be inside your head and how space helps you to process. It's a lot easier not take it personally when they realise this is how you cope in general.
Signs your need to process alone is attachment related:
You don't recall many incidences of your caregivers being able to effectively comfort you
Usually you have felt worse after opening up or you anticipate you'll feel worse if you do, even though you often feel better when you let yourself be heard by a safe person
You don't trust others to treat your vulnerabilities gently and to respect you
You feel unworthy of being supported
You feel defensive often
You think sharing your feelings is pointless -nobody will understand or help anyway. You just want people to get out of your way so you can solve things yourself.
Work on healing attachment trauma - e.g. work out what space protects you from feeling. Grieve the love you were not given in the past. Build self love. Find a professional to help.
Empathise with why it's difficult for your person when you take space. It probably triggers their abandonment trauma and they may feel unloved or untrusted.
Take a 30 minute break during conflict if you feel overwhelmed
Share information about conscious communication with your partner so you minimise any triggering
Let your partner know that you'll be back, and when.
Reassure them about the state of the relationship.. I love you, I'm not going anywhere etc.
Try shortening the time you take to process a little- lean into the discomfort and be courageous.