I am not sure that the company would be legally required to hire you under the circumstances you outline. In many jurisdictions it may well be able to argue that -- qualified though you may be -- you are less suitable than other candidates because you are less likely to be loyal to the company and hence likely to be less effective at promoting its business interests. Be this as it may, there is a clearer and cleaner example of your asymmetry: while you are free not to buy from the company, it is not free not to sell to you.
What's the moral rationale for this legal asymmetry? Strong versus weak may well have something to do with it -- and, relatedly, the fact that companies selling to individuals face millions of potential customers whereas individuals buying from companies may not have many to choose from (imagine you had protested against Microsoft and Gates then refused to license you to use Windows).
A further point is that companies are artificial agents created pursuant to constitutive rules laid down by the state. These rules are known in advance and those who do not want to create or purchase a company under such conditions can refrain. This element of voluntariness makes the burdens involved more acceptable. When you consider opening a business in the US, you know beforehand that you'll have to serve people whose skin color or religion differs from your own and you know beforehand that potential customers will be free to shop elsewhere even at higher prices. This element of voluntariness is absent in the case of individuals. Rosa Parks didn't decide to be born in the US on the understanding that businesses would be free not to serve her.
Another point is economic efficiency. It would be very costly for the legal system to ensure that individuals do not boycott businesses -- and it's very much less costly, by contrast, to enforce the rule that businesses must not refuse to serve willing customers. Conversely, permitting businesses to exclude potential customers is likely to be more costly to the economy (e.g., by forcing people to drive long distances to get served) than permitting customers to boycott businesses. (To be sure, much-disliked businesses may go under, but this is a large loss to their owners, not to the economy.)