You should only link to other websites if you think they'll be of value or interest to your readers - not because the other website links back.
If you want websites to link to your website, make your website worthy of being linked to.
Link to relevant websites only for your readers' sake, and then ask those websites for a link. But don't make your link back to them a requirement on whether they link back or not. If they're worth linking to, they're still worth linking to even if they don't link back to you.
Google judges relevance to the search query (keyword search phrases) by looking at 100s of features and only some of those we know. One factor is internal and external links. Use key focus phrases in the anchor tags for these links i.e. rather than using 'click here', try 'find out more about flower pots' as the link works.