Will updating a phrase hurt our rank

My company has a large website targeting a specific age group. That age group has changed. I asked our web agency to update those old phrases/ages throughout our website ASAP and they said they want to do it little by little or it will hurt our SEO rank. That doesn't sound right. I can't find anything online to support their claims. Am I right?

It is possible that updating phrases on your website could impact your SEO ranking, especially if the outdated phrases are heavily used in your search listing snippets. While it’s not confirmed that Google uses those specific phrases for ranking, it’s best to be cautious when making drastic changes to your website content. A slow rollout with testing could be a safer option. This way, you can assess the impact of the changes on your ranking and make adjustments if necessary.