A.W. Pink's Exposition Of Hebrews 2:9

That He by the grace of God should taste death for every man. (Hebrews 2:9 b).

 "That He by the grace of God should taste death for every man." The opening words of this clause set forth the efficient cause which moved the Godhead in sending forth the Son to submit to such unparalleled humiliation: it was the free favour of God. It was not because that the ends of Divine government required mercy should be shown to its rebels, still less because that they had any claim upon Him. There is nothing whatever outside God Himself which moves Him to do anything: "He worketh all things after the counsel of His own will." (Eph. 1:11). It was solely by the grace and good pleasure of God, and not by the violence of man or Satan, that the Lord Jesus was brought to the cross to die. The appointment of that costly sacrifice must be traced back to nothing but the sovereign benignity of God.

 "For every man." This rendering is quite misleading. "Anthropos," the Greek word for "man" is not in the verse at all. Thus, one of the principle texts relied upon by Arminians in their unscriptural contention for a general atonement vanishes into thin air. The Revised Version places the word "man" in italics to show that it is not found in the original. The Greek is "panta" and signifies "every one," that is, "every one" of those who form the subjects of the whole passage-every one of "the heirs of salvation" (Heb. 1:14), every one of the "sons" (Heb. 2:10), every one of the "brethren" (Heb. 2:11). We may say that this is the view of the passage taken by Drs. Gouge and J. Brown, by Saphir, and a host of others who might be mentioned. Theologically it is demanded by the "tasted death for every one," i.e., substitutionally, in the room of, that they might not. Hence, every one for whom He tasted death shall themselves never do (see John 8:52), and this is true only of the people of God. 

 What we have just said above is confirmed by many Scriptures. "For the transgression of My people was He stricken" said God (Isa. 53:8), and all mankind are not His "people." "I lay down My life for the sheep," said the Son (John 10:10), but every man is not of Christ's sheep (John 10:26). Christ makes intercession on behalf of those for whom He died (Rom. 8:34), but He prays not for the world (see John 17:9). Those for whom He died are redeemed (Rev. 5:9), and from redemption neccessarily follows forgiveness of sins (Col. 1:14), but all have not their sins forgiven.

Page 68 AN EXPOSITION OF HEBREWS (Wilder Publications).

No doubt those of an Arminian (free will mindset) will rail at the above, nevertheless it is Scriptural, that is it agrees with what the Scripture says. It cannot be gainsaid, unless one wants to deny what is plainly written. There are those who would deny Absolute predestination/election (such call us "Calvinists") nor will they affirm they are Arminians, they would simply call themselves "Biblicists"; but this will not do (as if neither of the aforementioned wouldn't assign such a term to their own theology!).

I often wonder why otherwise intelligent believers attack so-called Reformed Calvinistic theology with the ferocity that they do. They would do well to read the works of great Reformed teachers, Calvin, Zanchius, Edwards, Owen, Spurgeon, Newton, Ryle, Saphir, Pink, and a whole host of others beside. But then, I suppose if one hates stamp collecting, they are hardly going to buy books about the subject, are they?  I am sure there is a better analogy, but you get the gist?