I find this metaphor applicable especially to social anxiety, shyness, and frustrations finding new relationships.
The aspect of this metaphor I don't fully like is that it is a little bit "predatory". And I also feel badly for creatures that are hunted or raised for food, including fish. Yet, fishing has been an important human activity for thousands of years, and similar processes occur in all other domains of nature. Also, the metaphor of fishing has been used elsewhere in literature & religion (e.g. in a story from the Bible, Jesus' disciples are called to be "fishers of men"). In adopting this metaphor, I would insist that people maintain healthy, honourable respect for other individuals ("fish"), just as they would expect others to treat them honourably. But here is the metaphor:
Forming relationships is like fishing.
In order for fishing to be a positive and successful experience, it helps to enjoy the process: getting up early, traveling to the lake, organizing your equipment, sitting in the boat. If you enjoy the process itself, your emotions will be more relaxed and positive, and you will be less vulnerable to feeling hurt or disappointed if you don't actually catch any fish.
You should be well-fed, not hungry, when you get into your boat.
Once you are in the boat, you need to have your line in the water.
If you are not getting any bites, you may need to move your boat, or try a different lure.
If you have many bites, but no fish, it is usually a good sign, not a bad sign. Keep trying. Mind you, there may be a problem with your technique that is causing this problem, so you may need to assess this or get advice about it.
It is a recipe for disappointment if you expect to catch a particular individual fish that you see in the lake (you can always try, though, as long as the effort is enjoyable for you). Be open to assessing the bites that you actually get.
It can help immensely to have a "guide" to help you fish.
It is vitally important to learn about safety on the water, and to take all appropriate steps to stay safe (e.g. life jackets, learning boating skills, letting people know where you are, etc.).
It is necessary, healthy, and appropriate, to "throw back" fish that are not the right ones for you. You should be skilled at this practice, so that you do not unnecessarily injure yourself, or the fish you throw back.
Fishing is probably more enjoyable and a more successful activity if it is something you do regularly as part of a healthy lifestyle, instead of something you do only once every few years.