There's a multitude of interpretations there, but to me the obvious(TM) takeaway is that corporate taxes should be zeroed out for everyone, and income/consumption/environmental taxes (take your pick of weighting) increased to make up for it.
I'm probably stepping into a pre-existing argument, but forming a corporation allows me to gain benefits that would be difficult or impossible to obtain as an ordinary person. (e.g. limited liability, special tax treatment) It's not unreasonable that a corporation's owners pay additional taxes.
More like: "the politicians responsible for setting tax policy routinely end up abusing small companies with high taxes while rewarding big companies with low taxes and claims of Jobs Jobs Jobs (re-elect me!). the jobs are frequently a lie so mostly the big companies just get unfair advantages. this is manifestly unfair to small companies and to communities. maybe politicians shouldn't tax corporate activity at all -- besides the problems mentioned already it reduces incentives to invest and to have jobs in a location -- and we should get our taxes from economic activity once the money's left the corporation, like the executives' property, or a sales tax that penalizes excessive consumption, or carbon taxes -- which might also help the environment! and then maybe we should charge companies fees for the services that they use instead of general-fund spending so that companies have a harder time offloading costs onto the jurisdictions where they're hosted."
This is a fairly common economically-conservative public-policy position. It can be debated as desirable or undesirable, but!!! it is consistent and coherent and does attempt to achieve equity under the law. It's probably hardest to implement in a place like the US where there are multiple jurisdictions involved and the revenue from a sales tax or property tax could end up far away from the communities where the corporations impose costs (though the fee-for-services model does mitigate that).