Examiners can propose amendments that (in their view) place an application in condition for allowance. Such amendments almost universally come with formal notices of allowance and allowability, and usually follow a discussion with the applicant or applicant's counsel. See generally MPEP 1302.04 and 714(II)(E). Note that substantive amendments to the claims (which is the case in your specified situation) require applicant approval. See MPEP 714(II)(E) ("Authorization and appropriate extensions of time are required if the changes made in the examiner’s amendment are substantive (e.g., the examiner’s amendment would include a cancellation of a claim or change the scope of the claims").
So that raises the question: did you authorize the amendment made by the Examiner?
On another note, you asked about the basis for the Examiner's amendment. One possible basis, and the first that came to mind in your situation, is that the Examiner feels that the CIP (which includes identical claims as the parent) introduces a double patenting problem. In straightforward terms, a patent grants exclusive rights to the claimed invention. If two patent applications (or an issued patent and a patent application) have claims that are the same or which significantly overlap in scope, an issue arises where two patents could be issued with claims that cover the same subject matter. In other words, two patents could issue with the same "exclusive" rights. Provided it is aware of the issue, the PTO will not allow this to occur and will usually address this problem by issuing a double patenting rejection. See generally MPEP 804.
In your case, some claims of the CIP are identical to some claims of the parent. This introduces a "statutory" double patenting problem that can only be overcome by amending the claims of one of the two conflicting applications, or by abandoning one of the two conflicting applications. In your case, I am almost certain that the Examiner saw the double patenting issue, and has attempted to rectify it by amending the claims of the parent application (i.e., by adding claims 2 and 3 to claim 1). What the Examiner may not have explained to you, however, is that the double patenting issue could also be overcome by amending the claims of the CIP application, e.g., to claim only the added subject matter. While amending the CIP may not overcome the double patenting issue entirely, it would likely move the issue from a "statutory" double patenting rejection (which can only be overcome by amendment or abandonment of one of the applications, as noted above) to one of "non-statutory" obviousness type double patenting (NSODP). Unlike a statutory double patenting rejection, a NSODP rejection may be overcome by filing a terminal disclaimer (essentially, a document linking two applications that include claims of overlapping scope).
Amending the CIP is a longer route, and likely requires the Examiner to issue one or more additional rejections. Depending on the situation, this could prevent the examiner from receiving another "count" towards his quota from the parent application. This is probably why the Examiner suggested amending the claims of the parent, as opposed to amending the CIP as discussed above. However, amending the CIP might allow you to obtain significantly broader claims in the parent (i.e., original claim 1, as opposed to claim 1 including the elements of claims 2 and 3). If broader protection is desired (which it appears that it is), then amending the claims of the CIP would appear to be the avenue of interest to you.
Note that while you could theoretically obtain protection for unamended claim 1in the CIP, the claims of the CIP may not be entitled to the benefit of the priority date of the parent application. Thus, the claims of the CIP may be vulnerable to "intervening" prior art, i.e., art arising between the filing date of the parent and the filing date of the CIP. Pursuing unamended claim 1 in the parent completely avoids this issue.
Since you are pro se, I would call the Examiner and try to get him/her to explain the basis of the proposed examiner's amendment to you. If it is the double patenting issue I explain above, and if you want to obtain broader claims in the parent, ask the examiner to explain your options for objecting to the examiner's amendment and addressing the DP issue by amending the CIP application. You may have to file a response after notice of allowance (don't let the non-extendable deadline lapse).
Good luck, and don't hesitate to follow up with additional questions.
Best,
Klav
PS: While I am a patent attorney, I am not your patent attorney. Anything I post on these forums is not legal advice, and you rely on anything I say here at your own risk.