One possible reason could be to protect Teddy. Maybe there are some threats in England that Harry wants to keep Teddy away from. For example, there could be some dark wizards or dangerous magical creatures that target Teddy for some reason.
The fanfiction could show their journey as a very secretive one. They might be using various disguises and spells to avoid being detected. Harry, being a well - known figure, would want to keep their departure and journey under wraps to avoid any unwanted attention or interference.
In the fanfiction, it could be that Harry is taking Teddy away to protect him from something. There might be a new threat emerging in the wizarding world, and Harry, with his experience, decides to keep Teddy safe by leaving with him. They could end up at a secret location, where Harry starts to train Teddy in advanced magic, sharing all his knowledge and skills.
Maybe it's a group within the Ministry of Magic who oppose Harry's influence on Teddy. They might see Harry as trying to groom Teddy to be his successor in some way and want to stop them from leaving together to prevent this.
Maybe Harry leaves England to explore the wizarding world in other countries. He could go to France to study different magic spells at Beauxbatons Academy. Or perhaps he travels to America to help the MACUSA (Magical Congress of the United States of America) deal with some dark magic threats.
He could meet new witches and wizards from different cultures. For example, he might run into a powerful African wizard who has unique magical abilities related to nature magic. Or he could meet a Japanese witch who specializes in charm - making that is based on ancient Shinto beliefs.
One possible story could be that Harry leaves England due to some family feud and the pregnant woman he's involved with decides to follow him. Maybe she's a Muggle who discovers the wizarding world through him and they embark on a journey to a new place where they can raise their child in peace.
Well, Harry Potter is obviously one of the main characters. The other main character is often an original female character who is pregnant. She could be a witch that Harry has fallen in love with or a Muggle who got caught up in the wizarding world through Harry.
Perhaps it's a completely new character, a powerful and mysterious wizard who came into Harry's life. Their encounter led to Harry's pregnancy, and the fear of this unknown wizard's intentions and the reaction of the English wizarding community makes Harry leave England.
One possible plot could be that Harry Potter discovers he is pregnant (through some magical means perhaps) and decides to leave England because he wants to protect his unborn child from the dark forces that still lurk in the country. He might go to a far - off magical land where he can raise the child in peace and secrecy.