I have been working as a content writer fro some time but am at a disadvantage when a client asks me if I am a SEO expert. I know it's not that difficult to be one but I don't know whether I have to take a course to qualify as one or just work with a SEO firm to pick up the tricks. Please help.

There are a few courses available to help you become more knowledgeable in the field of SEO, and they might help you gain credibility with certain audiences. Web CEO is actually not one I would recommend, as it's run by a commercial enterprise and isn't to my knowledge backed by a credible SEO expert. Here are three that are offered by marketing organizations or backed by leading experts:
SEMPO Institute Advanced SEO Certification
Bruce Clay's SEO Toolset
DMA Search Engine Marketing Certification Program

If you feel that you need extra training or are trying to land an SEO job without a lot of experience I think these courses could help you do it. As a graduate of SEMPO Institute's Advanced SEO program one of the people who hires SEOs for our agency, I would say that having any of these certificates would give you an advantage over someone with similar experience who wasn't trained.

That said, as someone who has been a successful SEO for years prior to taking any certification course, I don't believe any course is necessary to become an SEO. There's plenty of information out there on blogs like SEOMoz and Search Insider, and at conferences like SMX and SES, and at this point in the game Google even has a resource to help white hat SEOs learn their trade. If you have read and understood the Google Webmaster Guidelines, and practiced them for a few months, you should be able to see some improvement in indexing and ranking digital content in order to drive traffic or revenue. And from my perspective, and the perspective of most SEOs and clients who hire us, that's the test of whether or not you're an SEO, not necessarily a training course.

Good luck! Always keep learning the trade because it changes with the search engine algorithms.

Best,
Bryson