I know that you know, but I’m sure someone will see this statement and confuse beta and correlation for the same concept. And to further your correlation comment-- the covariance of any variable with itself is equal to it’s variance.
The returns of an asset can be perfectly positively correlated with the market returns, but this doesn’t mean the asset’s beta is 1 (the standard deviations of the two variables would need to be equal as well). The reason that the market beta is 1 is because the covariance of market returns with itself [market returns] is equal to the variance of market returns, which is also the same as the denominator for beta.