does the executor have the right to decide who gets what and chose what he wants and then offer the rest to the other sibling?
Much of your answer lies within the Will itself and the language used by the decedent. It isn't uncommon at all for a Will to leave "my estate in equal shares to my two children." Take every probate asset owned by the decedent and draw a line down the middle of it. That's what you would be entitled to under the Will. Dad had a car? You get half a car. He left a house? You get half the house.
Obviously, while cash can easily be divided, many assets are not so easy to carve up. The Will might provide for the executor to distribute assets "in kind," which would allow far more flexibility in the management of the estate. $100k in cash to son A and $100k house to son B, or something similar. Many executors are afforded a significant amount of freedom in managing estates, while others are subjected to far more supervision by the Court.
The real trick comes down to items and assets that are difficult to appraise or assign a value to. In the end, communication and cooperation by all parties will avoid 99% of the headache that can come along with things like this. No, the executor cannot treat himself any better as a beneficiary than he can treat you as a beneficiary. But, if there is a dispute, the executor could very likely just liquidate everything and cut the money down the middle. Nobody really wins in that scenario, and so a good deal of horse-trading might be needed in order to honor the 50/50 language without selling some of the items that are difficult to allocate.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.
Estate Planning Attorney
This is tricky because the executor is someone who is inheriting. The executor has the legal authority to transfer the property. While he might not have the "right" to give to himself what he wants and leave everything else to you there might not be much you can do about it of your portion amounts to what could be described as "equally".