If you're even a bit serious about analyzing a stock -- whether you're going to use the Capital Asset Pricing Model (CAPM) or whether you're just trying to know the stock's beta to build up some intuition -- you should calculate the beta yourself. Calculating the beta yourself is easy to do and if you either aren't able to do it or are unwilling to do it, you should probably not even be thinking about analyzing stocks at all (instead, you should stick with a far more passive strategy that involves mutual funds and ETFs).
Any serious investor and financial market participants will always calculate the beta on his or her own even if just to do a double-check against a number provided from a third-party source. However, in case you need some reasons to calculate a stock's beta on your own, here are 4 good ones:
1. Calculating a stock's beta yourself will allow all relevant information (until the day of your beta calculation) to be factored in
By calculating the beta yourself, you can literally use all the relevant data available to you through today. A third-party provider will most likely have a time lag. This time lag can be a day our two at best, but it could be almost a quarter at worst. Do you really want to have a beta that is almost 3 months stale? That is a ridiculous proposition when you can easily calculate a beta that will capture every available data point - you can calculate a beta in the evening and capture that afternoon's market volatility in your calculation.
2. You'll get to choose your own time horizon for the beta calculation
The beta you want might vary depending on your investment time horizon. For long term investors who have higher risk tolerances, daily price movements might be irrelevant. For traders or more risk-averse investors, daily price changes might be very important. When you calculate your own beta, you can choose how far back you want to go in terms of obtaining your data (eg. your market and stock prices).
Deciding how far back to go is useful, but clearly more current data is more useful than old data - there's going to be a limit to how far back you'll ant to go. Regardless, choosing how far back you want to go gives you the ability to capture data points in idiosyncratic times that you might care about (eg. an earthquake, a recession, geopolitical conflict, an election, etc.)
3. Calculating a stock's beta yourself will allow you to decide on your own interval
The more important and interesting part of calculating your own beta is the ability to choose the tie interval between data points - you can use daily market and stock prices or you can go longer and choose weekly or even monthly prices. Going longer would likely require a longer time horizon so that enough data points exist to perform soldi statistical analysis, but you're really in control when you calculate your own beta and you can decide what you care about. If you think weekly price changes are more relevant to you than daily gyrations, you can easily use that when calculating your own beta instead of having to rely on the assumptions and desires of a third-party.
4. Calculating a stock's beta will build your intuition regarding stocks, return time series, risk, and finance in general
Finally, you should calculate your own beta because it's easy to do and it will build your intuition of what beta is and what it represents. The more intuition you have, the less likely you are to make foolish investing mistakes - the more intuition you have the less likely you are to be led astray.